find the focal length of concave mirror experiment

Focal length of a concave mirror – theory and experiment

Spherical mirror has two types – Concave mirror and Convex mirror . In this article, we’re going to discuss the focal length of a concave mirror . Though, the focal length of both types of mirrors has the same definition and units, but the signs of focal length are different for these two mirrors . Here, we have included all these key points. Again, there is an experiment to determine the focal length of a concave mirror. The lab data and conclusion for this experiment are also discussed here.

Define focal length of a concave mirror

The focal length of a mirror is defined as the distance of its focal point from its pole. The focal length of a concave mirror is negative in sign if we consider the traditional sign convention rule for the mirror and lens. By the statement a concave mirror of focal length f we mean that the distance of the focal point of the mirror from its pole is f .

Why is the focal length of a concave mirror negative?

Parallel rays coming from the object on the left side will converge at a point on the left side or negative side, after reflecting from the mirror. This point is nothing but the focal point. Thus, the focal distance is negative for a concave mirror.

How to find the focal length of a concave mirror?

Determining the focal length of concave mirror experiment with lab report and conclusion.

In this part, we’re going to discuss the experiment for determining the focal length of a concave mirror with a lab report and conclusion. The concept used is that the parallel rays coming from a large distance meet at a point which is the focal point of the mirror. Then the distance of that point from the mirror will be the focal length of the mirror.

Apparatus used

Ray diagram, experimental data (lab report).

Calculation:

Conclusion:.

The focal length of the concave mirror is 11 cm .

A concave mirror has a focal length of 20 cm. Find its radius of curvature. If an object is placed at 30 cm from the mirror, then find the image distance.

Now, using the mirror formula for concave mirror we get, {\color{Blue} \frac {1}{f} = \frac {1}{v} + \frac {1}{u}}

Then, from the above equation we get, the image distance as, v = 60 cm .

This is all from this article. If you have any doubts on this topic you can ask me in the comment section!

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CBSE Class 10 Science Lab Manual – Focal Length of Concave Mirror and Convex Lens

December 2, 2022 by Veerendra

EXPERIMENT 4(a)

Aim To determine the focal length of concave mirror by obtaining the image of a distant object.

Materials Required A concave mirror, a mirror holder, a small screen fixed on a stand, a measuring scale and a distant object (a tree visible clearly through an open window).

• Fix a concave mirror in the mirror holder and place it on the table near an open window. Turn the face of mirror towards a distant object (suppose a tree).
• Place the screen, fitted to a stand, infront of the concave mirror. Adjust the distance of screen, so that the image of the distant object is formed on it as given in the figure below. We can infer from the figure that a clear and bright image could be obtained if the distant object (a tree), is illuminated with sunlight and the screen is placed in the shade. A bright image of the Sun could also be obtained, if the sunlight is made to fall directly on the concave mirror.

• Measure the horizontal distance between the centre of the concave mirror and the screen with the help of a measuring scale.
• Record the observations in the observation table.
• Repeat the experiment two more times by obtaining the images of two different distant objects and measure the distance between the concave mirror and the screen in each case. Record them in the observation table.
• Find the mean value of the focal length for all the observations for different objects.

Observations And Calculations Least count of scale used = …………. mm = …………. cm

Focal length for first object (f 1 ) = ………… m Focal length for second object (f 2 ) = ………….. m Focal length for third object (f 3 ) = …………. m Mean focal length = \(\frac { { f }_{ 1 }+{ f }_{ 2 }+{ f }_{ 3 } }{ 3 }\) = ………… m

Result The approximate value of focal length of the given concave mirror is ………… m.

Precautions

• Concave mirror should be placed near an open window through which sufficient sunlight enters, with its polished surface facing the distant object.
• There should not be any obstacle in the path of rays of light incident on the concave mirror.
• If the image of the Sun has to be formed, then it should be focused on the screen only. The image of the Sun should never be seen directly with the naked eyes. Sunlight should never be focused on any part of the body as it can burn it.
• In order to obtain a sharp and clear image of the distant object on the wall/ground, it must be ensured that the object is well illuminated, so that amount of light incident on the concave mirror is sufficient to produce a well illuminated and distinct image.
• The measuring scale should be parallel to the base of both the stands.
• The mirror holder along with the mirror should be kept perpendicular to the measuring scale for precise measurements.

Sources of Error

• The measuring scale may not be parallel to the base of both the stands.
• The mirror holder, along with the mirror, may not be kept perpendicular to the measuring scale.
• Least count of measuring scale may not be correctly noted.
• Measurement of distance from pole may not be made accurate.

Viva – Voce

Question 1. How will you distinguish between a concave and a convex mirror? [NCERT] Answer: A concave mirror is the spherical mirror with inward curved reflecting surface, whereas a convex mirror is the spherical mirror with outward curved reflecting surface. Concave mirror forms a sharp image, whereas a convex mirror cannot form a sharp image of the distant object.

Question 2. To determine the focal length of a concave mirror, a student focuses a classroom window, a distant tree and the Sun on the screen with the help of a concave mirror. In which case will the student get more accurate value of focal length? [NCERT] Answer: Student will get more accurate value of focal length in the case of Sun.

Question 3. What will be the nature of the image formed by a concave mirror for a distant object? [NCERT] Answer: The nature of the image formed by a concave mirror for a distant object is real and inverted.

Question 4. In reflector type solar cookers, special concave (parabolic) mirrors are used. In such cookers, what should be the preferable position of food vessel for cooking? [NCERT] Answer: In reflector type solar cookers, the preferable position of food vessel should be at focus of the concave mirror.

Question 5. What type of mirror is used in torch? Give reasons. [NCERT] Answer: In torch, concave spherical or parabolic mirror is used because when the bulb (source) is kept at the focus of a concave mirror, parallel beam of light is obtained which travels a large distance.

Question 6. What type of mirror is used as a shaving mirror or in vanity boxes? [NCERT] Answer: Concave mirror is used as a shaving mirror or in vanity boxes, because when the object is placed between its focus and pole, the magnified, erect and virtual images of the object will be formed.

Question 7. Give the condition to hold a mirror for finding the focal length of the concave mirror. Answer: While holding the mirror for finding the focal length of the concave mirror, the aperture of the mirror must not be obstructed.

Question 8. Give the position of an object to obtain a virtual, erect and an image larger than the object using a concave mirror. Answer: The object should be placed between the focus and pole of the mirror.

Question 9. Why do we obtain blurred image from a concave mirror sometimes? Answer: The reason behind the blurred image is that the mirror is away from the object.

Question 10. How can we find the focal length of a concave mirror, when the image is obtained by using a concave mirror? Answer: Focal length can be found out by measuring the distance between the mirror and the screen.

Question 11. Why do we use a screen for obtaining an image from a concave mirror? Answer: Since, the image formed by the mirror is real, it can be obtained on a screen.

Question 12. Is the centre of curvature a part of a spherical mirror? Comment in support of your answer. Answer: The reflecting surface of a spherical mirror forms a part of a sphere. This sphere has a centre. This point is called the centre of curvature of the spherical mirror. So, it is not a part of the mirror as it lies outside its reflecting surface.

Question 13. Which surface of a shining spoon should be polished, to use the spoon as a concave mirror? Answer: The surface of the spoon which is bulged outward should be polished to use the spoon as a concave mirror.

Question 14. When the light of the Sun is directed on a sheet of paper with the help of a mirror, then the paper starts burning. Why? Answer: The light from the Sun is converged at a point, as the sharp, bright spot by the mirror. Actually, this spot of light is the image of the Sun on the sheet of paper. The heat produced due to concentration of sunlight ignites the paper.

Question 15. All the rays of light, after reflection from a concave mirror meet at a point infront of the mirror. Name this point. Answer: When parallel rays of light fall on a concave mirror along its axis, then the rays meet at a point infront of the mirror after reflection from it. This point is called the focal point.

Question 16. How does the size of the image vary as an object is moved from close to the pole to a large distance? Answer: Size of the image decreases as the object is moved away from the pole to a large distance. The image will be virtual for the object between the pole and the focus.

Question 17. State the importance of pole of a mirror. Answer: Pole is the mid-point of the mirror which makes the incident light to go at some angle on the other side of principal axis.

EXPERIMENT 4(b)

Aim To determine the focal length of convex lens by obtaining the image of a distant object.

Apparatus/Materials Required A thin convex lens, a lens holder, a small screen fixed on a stand and a measuring scale.

• Fix a thin convex lens on the lens holder and place it on the table same as that done in the case of concave mirror.
• Place the screen fixed to a stand on the other side of the lens. Adjust the position of screen by moving it back and forth in front of the convex lens to get a sharp and clear image of the distant object.

• Now, measure the horizontal distance between the centre of the convex lens and the screen with the help of a measuring scale.
• Repeat this experiment two more times by obtaining the images of two different distant objects and measure the distance between the convex lens and the screen and record them in the observation table.
• Find the mean value of the focal length for all the observations, for different objects.

Observation Table Least count of scale used = ………… mm = ………… cm

Calculations Focal length for first object (f 1 ) = ………… m Focal length for second object (f 2 ) = ………… m Focal length for third object (f 3 ) = ……………. m Mean focal length or approximate focal length of lens (f) = \(\frac { { f }_{ 1 }+{ f }_{ 2 }+{ f }_{ 3 } }{ 3 }\)

Result From the above observations and calculations, the approximate value of focal length of the given convex lens is ………. m.

• The principal axis of the convex lens should be horizontal, i.e. the lens should be placed vertically.
• There should be no obstacle in the path of rays of light from the distant object incident on the convex lens.
• The image of the sun formed by the lens should be focussed only on the screen. The image of the sun should never be seen directly with the naked eye or it should never be focussed with a convex lens on any part of the body, paper or any inflammable material as it can burn.
• Sometimes, the parallel rays of light originating from a distant object and incident on a convex lens may not be parallel to its principal axis. The image in such situation might be formed slightly away from the principal axis of the lens.
• The base of the stands of the convex lens and screen should be parallel to measuring scale. To determine the focal length, the distance between the convex lens and the screen should be measured horizontally.
• The principal axis of convex lens may not be in horizontal position.
• There may be some obstacle in the path of light ray, coming from the distant object.

Question 1. How will you distinguish between a convex and concave lens? [NCERT] Answer:

  Question 2. To determine the focal length of a convex lens, a student focusses a classroom window, a distant tree and the Sun on the screen. In which case, will the student is closer to accurate value of focal length? [NCERT] Answer: In the case of Sun, because it works as an infinite object and rays will be perfectly parallel to the principal axis.

Question 3. What is the nature of an image formed by a thin convex lens for a distant object? What change do you expect, if the lens were rather thick? [NCERT] Answer: The nature of an image is real, inverted and diminished. If lens becomes thicker, only focal length of lens decreases.

Question 4. You are provided with two convex lenses of same aperture and different thickness. Which one of them will be of shorter focal length? [NCERT] Answer: A thick convex lens has shorter focal length.

Question 5. |f we cover one-half of the convex lens, while focussing a distant object, in what way will it affect the image formed? [NCERT] Answer: If we cover one-half of the convex lens, there will be no change in the nature of lens, only intensity of the image formed decreases.

Question 6. Can this method be used to find the approximate focal length of the concave lens? [NCERT] Answer: No, this method cannot be used to find the approximate focal length of the concave lens, because it always forms a virtual image.

Question 7. Which type of lens is used by the watchmakers, while repairing five parts of a wrist watch? [NCERT] Answer: Watchmakers use convex lens, and to obtain enlarged image, they place the object between optical centre and focal length.

Question 8. Give the complete detail of the nature of image so formed in this experiment. Answer: The nature of image formed in this experiment is as follows:

Question 9. When a ray of light emerges out from a denser medium of the lens, how will it bend into the rarer medium of air? Answer: It bends away from the normal at the point of incidence on the interface.

Question 10. How will a ray of light falling on a denser medium of convex lens bend? Answer: It bends towards the normal at the point of incidence on a denser medium of lens.

Question 11. What happens to a ray of light when it passes through the optical centre of a lens? Answer: When a ray of light passes through the optical centre of a lens, it goes without bending.

Question 12. State whether the nature of image formed by a convex lens depends on the position of object. Answer: Yes, it forms virtual image only when placed between focus and optical centre and for all other positions, it forms real image.

Question 13. On what factor, does the ability of a lens to converge or diverge the light rays depend? Answer: It depends upon the focal length of the lens.

Question 14. If the lens used in the experiment is a plano-convex lens, then what is the radius of curvature of the plane surface? Answer: The radius of curvature of the plane surface of plano-convex lens is infinity.

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NCERT Class 10 Science Lab Manual Focal Length of Concave Mirror and Convex Lens

CBSE Class 10 Science Lab Manual Focal Length of Concave Mirror and Convex Lens

NCERT Class 10 Science Lab Manual – Focal Length of Concave Mirror and Convex Lens

Physics Practical Class 10 Introduction Light shows the property of reflection and refraction. Reflection: The bouncing back of light on hitting any medium/surface is called reflection of light.

• The angle of incidence is equal to the angle of reflection.
• The incident ray, the reflected ray and the normal ray lie in the same plane. > Mirrors: A smooth, silver surface which reflects light regularly is called a mirror.

Types of mirror

• Concave mirror: The spherical part of the sphere which is painted from the outer side is called concave mirror.
• The concave mirrors are used as shaving mirrors as they magnify objects placed close to them.

• Convex mirror: The spherical part of the mirror which is painted from the inner side is called convex mirror.
• The convex mirrors are the side view mirrors of cars. These types of mirrors have wider fields of view than flat mirrors, but objects appear smaller in them.

• Pole: The pole is defined as the geometric center of the curved mirror.

• Radius of curvature: The radius of curvature of a curved mirror is defined as the radius of the hollow glass sphere of which the spherical mirror was a part. In the figure given above, the distance between ‘P’ and ‘C’ is the radius of curvature ‘R’.
• Principal axis: The principal axis of a curved mirror is defined as the imaginary line passing through its pole P and centre of curvature C.
• Principal focus: The principal focus (denoted by F in the figure) is defined as the point on the principal axis where the light rays traveling parallel to the principal axis after reflection actually meet (for a concave mirror) or appear to meet (for a convex mirror).
• The principal focus is in front of the concave mirror and is behind the convex mirror.
• Focal length: The focal length (denoted by FP in the fig.) is the distance between the pole P and the principal focus F of a curved mirror.
• The focal length is half the radius of curvature. Focal length = Radius of curvature/2 .

Rules for constructing ray diagrams

• Any light ray traveling parallel to the principal axis is reflected by the curved mirror through the principal focus. It either actually passes (for a concave mirror) or appears to pass (for a convex mirror) through the principal focus.
• Any light ray that passes (for a concave mirror) or appears to pass (for a convex mirror) through the principal focus is reflected by the curved mirror parallel to the principal axis.
• Any light ray that passes (for a concave mirror) or appears to pass (for a convex mirror) through the center of curvature retraces its initial path after reflection by the curved mirror.

Important terms related to Lens

• Principal Axis: The principal axis is a line that is perpendicular to and passes through the centre of the lens.
• Principal Focus: The principal focus, F is the point through which all incident rays travelling parallel to the principal axis after refraction appear to meet.
• The focal length: “f ’ is the distance from the centre of the lens, O to the principal focus, F.

Rules for constructing ray diagrams:

• A ray from the top of the object proceeding parallel to the centerline is perpendicular to the lens. It-will pass through the lens and the principal focal point.
• A ray through the center of the lens, will pass straight through the lens.
• A ray passing through the principal focal point of the lens will proceed parallel to the centre line upon exit from the lens.

CBSE Class 10 Science Lab Manual Experiment – 4

Aim To determine the focal length of (i) concave mirror (ii) convex lens by obtaining the image of a distant object.

Theory Focal length of Concave Mirror

• A spherical mirror, whose reflecting surface is curved inwards, that is, faces towards the centre of the sphere, is called a concave mirror.
• A concave mirror, like a plane mirror, obeys the laws of reflection of light.

• When parallel rays of light fall on a concave mirror along its axis, the rays meet at a point in front of the mirror and the image formed of the object is real, inverted and very small in size.
• As the image formed by concave lens is real it can be obtained on a screen.
• The distance between the principal axis P of the concave mirror and the focus F is the focal length of the concave mirror. It is denoted by letter ‘f’.

Rules for Obtaining Image Formed By Concave Mirror

• A ray of light parallel to principal axis of a concave mirror, passes through its focus after reflection from the mirror as shown in figure (i).
• A ray of light passing through the centre of curvature of a concave mirror is reflected back along the same path as shown in figure (ii).

Focal Length of Convex Lens

• When a parallel beam of light falls on a convex lens, the rays, after refraction converge at a point on its other side.
• If the parallel beam of light comes from a distant object, a real, inverted image of very small size is formed at the focus of the lens.
• The distance between the optical centre of lens ‘O’ and the principal focus ‘F’ of the lens is called focal length of a lens, ‘f’ is the representation of focal length.
• Since the image formed by the lens is real, it can be obtained on a screen.
• Types of Images:

To Determine The Focal Length Of Concave Mirror Practical

(i) To determine focal length of a given concave mirror:

Materials Required A concave mirror, a measuring scale, a screen a mirror holder and mirror stand.

• Select a distant object from the laboratory window (distance should be more than 50 ft).
• Fix the concave mirror on the mirror stand placed on the table, facing the distant object.
• Place the screen in front of the reflecting surface of the mirror. Move the screen back and forth until a clear, sharp image of the distant object is obtained on the screen.
• Measure the distance between the concave mirror and the screen with a metre scale. This distance is the focal length of the given concave mirror. Record the focal length.

Observation Table

Result The focal length of the given concave mirror = 10 cm

Precautions

• The distant object must be well illuminated to produce a well illuminated and distinct image.
• Always place the concave mirror near an open window.
• The polished surface of the concave mirror must face the distant object.
• There should be no obstacle or hurdle in the path of rays of light from the distant object, incident on the concave mirror.
• The base of the stands of the concave mirror and screen should be parallel to the measuring scale.
• The mirror holder along with the mirror should be kept perpendicular to the measuring scale for precise measurements.

Focal Length Of Convex Lens Experiment Class 10

(ii) To determine focal length of a given convex mirror:

Materials Required Wooden bench, convex lens, a lens holder, a screen fixed to a stand, a measuring scale; etc.

• Arrange the wooden bench capable of holding the lens and screen horizontally on a table, so that the lens and screen are not disturbed.
• Keep the lens in a holder facing a distant object say tree branches.
• Fix the screen on another holder and keep it on the bench.
• Adjust the position of the screen in such a way that a sharp image of the given distant object falls on it.
• Note down the position of the lens in the table and the screen, and find the differences and record the same. The difference will give the focal length of the given convex lens.
• Focus the lens towards various distant objects and repeat the experiment to find the position of sharp image and thereby the focal length.

Result The focal length of the given convex lens = 10 cm

• Convex lens should be placed vertically.
• There should be no obstacle or hurdle in the path of rays of light from the distant object incident on the common lens.
• In order to get a well illuminated and distinct image, it must be ensured that the distanct object is well illuminated.
• The base of the stands of the convex lens and screen should be parallel to the measuring scale.

NCERT Class 10 Science Lab Manual Viva Voce

Question 2: Name two types of spherical mirrors. Answer: Concave mirror and convex mirror.

Question 3: Which mirror always produces virtual image? Answer: Plane mirror and convex mirror.

Question 4: Define aperture of a spherical mirror. Answer: It is the diameter of the circular rim of a spherical mirror.

Question 5: Define centre of curvature of a spherical mirror. Answer: The centre of the hollow sphere of which spherical mirror is a part is called the centre of curvature.

Question 6: What is the relation between focal length T and the radius of curvature ‘R’ of a concave mirror? Answer: f = R/2.

Question 7: What is meant by principal axis of a spherical mirror? Answer: The imaginary line passing through the pole and the principal focus of the spherical mirror is called its principal axis.

Question 8: What is the pole of a concave mirror? Answer: It is the centre point of the reflecting surface of the concave mirror. It is represented as ‘P’.

Question 9: What is centre of curvature of a concave mirror? Answer: Centre of curvature ‘C’ is the centre of the sphere of which the concave mirror forms a part.

Question 10: What is radius of curvature of concave mirror? Answer: Radius of curvature is the radius of the sphere of which the mirror forms a part.

Question 11: What is the principal focus (F) of the concave mirror? Answer: A point in front of a concave mirror where a beam of light parallel to the principal axis converge.

Question 13: What is the law of reflection for mirror? Answer: (i) The incident ray, the reflected ray and the normal, all lie in the same plane. (ii) ∠i = ∠r

Question 14: How many refracting surfaces does a lens have? Answer: Two

Question 15: Name two types of lenses commonly used. Answer: Convex lens and concave lens.

Question 16: Is focal length of a convex lens taken +ve or – ve? Answer: Positive, since it converges light.

NCERT Science Lab Manual Practical Based Questions

Question 1: Just by looking at an object, how do you come to know whether it is a smooth surface or rough one? Answer: When the object is smooth, reflection is regular and the object shines. When the object is rough, reflection is irregular, the object appears to be dull.

Question 2: What type of image is formed by a plane mirror? Answer: Plane mirror forms a virtual image, and, lies as far behind the mirror as the object lies in front of it and is laterally inverted.

Question 3: An incident ray makes an angle of 40° with the plane mirror, what is the angle of reflection? Answer: The angle of incidence in this case would be 50°, hence the angle of reflection will be 50°.

Question 4: Which mirror forms a real focus and why? Answer: Concave mirror forms a real focus because it is a converging mirror. All the light rays incident on it converge and actually meet at one point on the principal axis.

Question 5: Give one condition when concave mirror does not form a real image. Answer: When the object is placed between the focus and pole of the concave mirror, the image formed is virtual.

Question 6: Convex mirror is a diverging mirror so it does not form a real focus. But plane mirror is not a diverging mirror, why does it not form a real focus. Answer: In case of plane mirror, the incident rays and the reflected rays form same angle with the mirror and the reflected rays do not converge. So, it forms a virtual image.

Question 7: State the position of an object if you want to obtain an image of same size in case of concave mirror. A nswer: The object should be placed at ‘C’ of the concave mirror.

Question 8: Name the mirror used for shaving and why? Answer: The concave mirror is used for shaving because when an object is placed between the pole and the focus of the mirror, the image formed is virtual and highly magnified.

Question 9: You are standing facing a mirror and your image appears to be as follows: Head – appears to be very big Body – appears to be of same size Legs – appear to be very small. How will you explain for such an image formation? Answer: The mirror in this case is combination of three mirrors. The top part is a concave mirror, the middle part is a plane miiTor and the bottom part is a convex mirror.

Question 10: Name two spherical mirrors. Answer: Concave mirror and convex mirrors are spherical mirrors.

Question 11: What is the relation between the focal length and radius of curvature for concave mirror? Answer: The focal length is ‘f’ and radius of curvature is ‘R’ of concave mirror and f = R/2.

Question 12: Give two uses of concave mirror. Answer: Concave mirror is used by dentist and in solar cooker.

Question 13: What type of image does a concave mirror forms? Answer: Concave mirror forms a real image.

Question 14: If the object is at infinity where will the image be formed in case of concave mirror? Answer: The image will be formed at the focus ‘F’.

Question 15: When does concave mirror form a virtual image? Answer: Concave mirror will form a virtual image when the object is placed between pole and the focus.

Question 16: In case of concave mirror give the sign convention for ‘f’. Answer: The ‘f is negative when the image formed is real and T is positive when the image formed is virtual.

Question 17: When parallel beams fall on a convex lens, what happens? Answer: It converges at focus of the convex lens.

Question 18: When light passes through optical centre of a convex lens, what happens to it? Answer: It will go without deviating.

Question 19: Does the nature of image formed by a convex lens depend on the position of object? Answer: Yes, it forms virtual image only when placed between focus and optical centre and for all other positions it forms real image.

Question 20: How will you distinguish a concave lens from a convex lens experimentally? Answer: If the given lens forms sharp real image of a distant object, it is convex lens. Otherwise, it is a concave lens.

Question 21: If we cover the one half of the convex lens while focussing a distant object, will it affect the image formed? Answer: Image will be formed, as usual but the intensity will be reduced to half the original.

Question 22: Which out of the two spherical mirrors, has positive focal length? Which of the two will form real and inverted image at its ‘F’ point, which can be taken on the screen? Answer: Convex mirror has positive focal length. Concave mirror forms a highly diminished sized, real and inverted image of the object at ‘F’ point which can be taken on the screen.

Question 23: What is the nature of the image formed by a concave lens? Can this be taken on the screen? Answer: A concave lens always forms erect and virtual image of the object. The image formed is diminished in size. The image cannot be taken on the screen.

Question 24: For finding the focal length of a concave mirror, where do we keep the object? What is the position of image formed? On which structure we get the image? What is the nature of the image formed? Answer: A large sized object placed at a far off (Infinity) place, seen from the window of the lab, is taken as object. The image is formed at F point of the mirror. This image is formed on the screen. The distance between the mirror and the screen is measured; which is equal to focal length of the mirror. The image formed is real and inverted.

NCERT Science Lab Manual LAB MANUAL QUESTIONS

Question 1: How will you distinguish between a concave and a convex mirror? Answer: The differences between concave and convex mirror are:

Question 2: To detemine the focal length of a concave mirror, a student focuses a classroom window, a distant tree and the sun on the screen with the help of a concave mirror. In which case will the student get more accurate value of focal length? Answer: To get the accurate focal length of any mirror the object should be placed at infinity. Hence, if sun is focused for getting the focal length than it would give better and accurate result.

Question 3: What will be the nature of image formed by a concave mirror for a distant object? Answer: The nature of image formed by the concave mirror is real and inverted for distant object.

Question 4: In reflector type solar cookers, special concave (parabolic) mirrors are used. In such cookers, what should be the preferable position of food vessel for cooking? Answer: In reflector type solar cooker, the position of food vessel should be at the focus of concave mirror.

Question 5: What type of mirror is used in a torch? Give reasons. Answer: In torch behind the bulb a concave spherical mirror is placed so that the parallel beam of light is reflected by it which travels a large distance.

Question 6: What type of mirror is used as shaving mirror or in vanity boxes? Answer: Concave mirror is used as shaving mirror or in vanity boxes because it gives magnified, virtual and erect image.

Question 7: How will you distinguish between a convex and concave lens? Answer:

• Convex lens is bulging out from both the sides whereas concave lens is curved inside from both the sides.
• Convex lens forms a real focus and the distant object’s real, image is formed on the screen but concave lens do not form a real focus and the image formed is virtual.

Question 8: To determine the focal length of a convex lens, a student focuses a classroom window, a distant tree and the sun on the screen. In which case will the student is closer to accurate value of focal length? Answer: The accurate value of the focal length would be obtained by focusing the sun on the screen.

Question 9: What is the nature of an image formed by a thin convex lens for a distant object? What change do you except if the lens were rather thick? Answer: The image formed will be real, diminished and inverted. If the lens were thick then the nature of the image formed will be the same but focal length will be different.

Question 10: You are provided with two convex lenses of same aperture and different thickness. Which one of them will be of shorter focal length? Answer: Thin lens will have shorter focal length.

Question 11: If we cover one half of the convex lens while focusing a distant object, in what way will it affect the image formed? Answer: The image will be formed completely but it will be blurred.

Question 12: Can this method be used to find the approximate focal length of a concave lens? Answer: No, concave lens does not form a real focus.

Question 13: Which type of lens is used by the watch-makers while repairing fine parts of a wrist watch? Answer: Convex lens, as it is used as magnifying lens.

Class 10 Science Lab Manual MULTIPLE CHOICE QUESTIONS (MCQs)

Questions based on Procedural and Manipulative Skills Question 1: The diameter of a spherical mirror is called (a) radius of curvature       (b) aperture (c) focal plane                      (d) pole Answer: (b) Explanation: The diameter of a spherical mirror is called its aperture.

Question 2: The distance between the pole and the principal focus of a concave mirror is called (a) focus         (b) focal length (c) pole           (d) radius of curvature Answer: (b) Explanation: It is the point where all the reflected rays meet.

Question 3: The image formed by a mirror is always virtual. It is (a) convex mirror (b) plane mirror (c) concave mirror (d) both convex and plane mirrors Answer: (d) Explanation: Both mirrors don’t form real focus, the rays after reflection do not meet.

Question 4: For a plane mirror, radius of curvature ‘R’ is (a) R = infinity (b) R=f/2 (c) R = 2f (d) R = 0 Answer: (a) Explanation: For plane mirror, R is at infinity.

Question 5: The mirror used in solar cooker is (a) any spherical mirror        (b) concave mirror (c) convex mirror                    (d) none of these Answer: (b) Explanation: All the rays after reflection meet at a point.

Question 6: The radius of curvature and focal length of a concave mirror are (a) positive (b) one is positive and other is negative (c) negative (d) none of these. Answer: (c) Explanation: Both are calculated against the direction of light/ it is Cartesian sign convention.

Question 7: A beam of parallel rays after falling obliquely in a plane surface (a) diverges (b) remains parallel but deviates (c) converges (d) remains parallel but does not deviate Answer: (b) Explanation: Plane surface will reflect the rays, but they will remain parallel.

Question 8: For a plane mirror, the radius of curvature R is: (a) R = ∞ (b) R = 0 (c) R = 2f (d) R = 2/f Answer: (a) Explanation: R is infinity for plane mirror.

Question 9: An object is placed at ‘C’, i.e., centre of curvature of a concave mirror. The distance between the pole of the mirror and the image formed is: (a) between f and 2f             (b ) equal to f (c) equal to 2f                       (d) greater than 2f. Answer: (c) Explanation: If object is at C, then the image if formed at C and C = 2f.

Question 10: What type of image is formed on our retina? (a) Plane               (b) Real (c) Virtual             (d) Magnified. Answer: (b) Explanation: On retina real and inverted image is formed.

Question 11: A concave mirror forms a real image of the given object. The magnification would be: (a) positive (b) negative (c) both (a) and (b) (d) none of these Answer: (b) Explanation: If the image is below the principal axis then magnification is negative.

Question 12: Image formed by a convex mirror is always: (a) real and diminished (b) real and magnified (c) virtual and diminished (d) virtual and magnified. Answer: (c) Explanation: Convex mirror does not form real focus.

Question 13: For a concave mirror: (a) ‘f’ is always positive          (b) ‘f’ is always negative (c)  ‘f’ can be +ve or -ve           (d) ‘f’ is both +ve and -ve Answer: (b) Explanation: The focal length of concave mirror is always negative, as per sign convention.

Question 15: A ray of light falls on the mirror and after reflection it takes the same path. The incident ray is: (a) passing through C                (b) through F (c) both (a) and (b)                    (d) through P Answer: (a) Explanation: Any ray that is passing through C will be reflected back in same path.

Question 16: The lens called as a magnifying glass is (a) convex lens                   (b) concave lens (c) concave mirror             (d) convex mirror Answer: (a) Explanation: Convex lens gives enlarged image when object is placed between F and pole.

Question 17: If you are to determine the focal length of a convex lens, you should have [Outside Delhi 2012] (a) a convex lens and a screen (b) a convex lens and a lens holder (c) a lens holder, a screen holder and a scale (d) a convex lens and a screen, holders for them and a scale. Answer: (d) Explanation: Screen is used to collect the real image and scale to measure the focal length.

Question 18: A student has to determine the focal length of a convex lens by obtaining the image of a distant object on a screen. Which of the following measures should he take to obtain better results? (i) Select a lens of small diameter (say 3 cm). (ii) Select a lens of larger diameter (say 5 cm). (iii) Select an object very far from the lens. (iv) Select an object far, but not very far, from the lens. (v) Keep all the lights of the room on. (vi) Keep minimum lights of the room on. (a) (i), (iii) and (v)                   (b) (ii), (iv) and (vi) (c) (i), (iv) and (vi)                  (d) (ii), (iv) and (v) Answer: (b) Explanation: To obtain the best focal length, keep the light dim, object far but not very far.

Question 19: To determine the focal length of given convex lens by obtaining a sharp image of a well lit distant object on a screen, a student generally follows the following steps which are not in proper sequence. (I) Adjust the position of the lens to obtain a sharp image. (II) Select a well lit distant object. (III) Hold the lens between the object and the screen. (IV) Place a screen opposite to the object on the lab table. (V) Measure the distance between the lens and the screen. The correct sequence of these steps are: (a) II, III, IV, I, V           (b) II, IV, III, I, V (c) II, III, I, IV, V           (d) II, I, III, IV, V Answer: (b) Explanation: It is the right sequence of the procedure.

Question 20: A sharp image of a distant object is obtained on a screen using a convex lens. In order to determine the focal length of the lens; we need to measure the distance between the (a) object and the lens (b) object and its image (screen) (c) lens and the image (screen) (d) lens and the screen and also object and the screen Answer: (c) Explanation: f= Distance between the image obtained and the reflector / mirror/ lens.

Question 21: To find the focal length of a concave mirror, Sita should choose which one of the following set-ups? (a) A mirror holder and a screen holder (b) A screen holder and a scale (c) A mirror holder, a screen holder and a scale (d) A screen, a mirror, holders for them and a scale Answer: (d) Explanation: Screen is used to collect the real image and scale to measure the focal length.

Question 22: To determine the focal length of a convex lens by obtaining a sharp image of a distant object we generally follow the following steps which are not in proper sequence. [Delhi 2012] (I) Hold the lens between the object and the screen. (II) Measure the distance between the lens and the screen. (III) Select a well lit distant object. (IV) Place a screen opposite to the object on the lab table. (V) Adjust the position of the lens to form a sharp image. The correct sequence of these steps is: (a) III, I, IV, V, II               (b) III, IV, I, V, II (c) III, IV, V, I, II                (d) III, I, V, IV, II Answer: (b) Explanation: It is the right sequence of the procedure.

Question 23: A student has to determine the focal length of a concave mirror by obtaining the image of a distant object on a screen. For getting the best result he should focus (a) a distant tree or an electric pole (b) a well-illuminated distant building (c) well-lit grills of the nearest window (d) a burning candle placed at the distant edge of the laboratory table Answer: (a) Explanation: The object should be not very far and well lit.

Questions based on Observational Skills Question 24: A concave mirror gives virtual, erect and enlarged image of the object when placed (a) at infinity                     (b) between F and C (c) between F and P          (d) at F Answer: (c) Explanation: When object is placed between F and P, then the reflected rays do not really meet.

Question 25: The image formed by a plane mirror is always (a) real and erect (b) real and inverted (c) virtual and erect (d) virtual and inverted Answer: (c) Explanation: Plane mirror has virtual focus.

Question 26: The mirror that always gives a virtual image and the image is smaller w.r.t. object, then the mirror is (a) concave          (b) convex (c) plane               (d) none of these. Answer: (b) Explanation: Convex mirrors always form diminished images.

Question 27: The object when placed at the focus of the concave mirror, the image is formed at (a) infinity           (b) centre of curvature (c) focus              (d) between F and O Answer: (a) Explanation: The rays after reflection do not meet in this case.

Question 30: The mirror used in car head light is: (a) concave          (b) convex (c) plane               (d) concavo-convex. Answer: (a) Explanation: Concave mirror acts as reflectors to focus light.

Question 31: An object is placed at the centre of curvature of a concave mirror. The image will be formed: (a) at C                              (b) beyond C (c) between F and C       (d) at F. Answer: (a) Explanation: If object is at C, then the image is also formed at C.

Question 32: To find the focal length of a concave mirror Rahul focuses a distant object with this mirror. The chosen object should be: (a) a tree                (b) a building (c) a window          (d) the Sun Answer: (a) Explanation: The object should be far but not very far.

Question 33: For finding the focal length of a convex lens by obtaining the image of a distant object, one should use as the object (a) a well lit distant tree (b) window grill in the class room (c) any distant tree (d) a lighted candle kept at the other end of the table Answer: (a) Explanation: The light and distance of the object is important consideration for correct focal length.

Question 36: An incident ray makes an angle of 30° with the surface of the plane mirror. The angle of reflection is (a) 30°              (b) 90° (c) 60°               (d) 0° Answer: (c) Explanation: The angle of reflection is 60 degrees. Note that the angle of incidence is not 30 degrees; it is 60 degrees since the angle of incidence is measured between the incident ray and normal.

Question 38: A convex mirror has focal length of 15 cm. An object is placed at 20 cm from the pole of this lens. The nature of the image formed will be. (a) virtual, erect and diminished (b) virtual, erect and enlarged (c) real, inverted and diminished (d) real, inverted and enlarged. Answer: (a) Explanation: Convex mirror forms virtual image when object is placed beyond focus.

Question 39: In a village fair a child sees his image as normal face, swollen body and very thin legs. The correct combination of mirrors is: (a) plane, convex and concave mirror (b) concave, plane, convex mirror (c) plane, concave and convex mirror (d) convex, concave and plane mirror. Answer: (c) Explanation: Plane mirror gives image of same size, concave mirror enlarges the image and convex mirror gives diminished image.

Question 40: Two plane mirrors are placed opposite to each other and a candle is placed in between, the image formed will be: (a) real and infinite (b) virtual and infinite (c) real and magnified (d) virtual and diminished. Answer: (b) Explanation: Two plane mirrors at opposite position will reflect the images at infinity, virtual image is formed by the plane mirror.

Question 41: The image formed at focus of a concave mirror is real, inverted, highly diminished. The object is: (a) at C (b) at infinity (c) between F and C (d) beyond C. Answer: (b) Explanation: If the object is placed at infinity, the image is formed at focus.

Question 42: When an object is placed at a distance 2f from the optical centre of the convex lens, its image will be formed at a distance. (a) f                  (b) 2f                 (c) f/2             (d) 3f/2 Answer: (b) Explanation: If the object is placed at 2f then the image will be formed at 2f.

Question 43: If an object is placed between the focus and pole of a convex lens, it forms (a) a real and diminished image (b) a virtual and diminished image (c) a virtual and enlarged image (d) a real and enlarged image Answer: (c) Explanation: If object is between F and pole of convex lens then the image formed is enlarged and virtual.

Question 44: To determine focal length of a concave mirror a student obtains the image of a well lit distant object on a screen. To determine the focal length of the given concave mirror we need to measure the distance between: (a) mirror and the object (b) mirror and the screen (c) screen and the object (d) screen and the object and also mirror and the screen Answer: (b) Explanation: l= distance between lens and the image.

Question 47: A student has obtained the image of a distant object with a concave mirror to determine its focal length. If he has selected a well illuminated red building as object, which of the following correctly describes the features of the image formed? (a) Virtual, inverted, diminished image in red shade (b) Real, erect, diminished image in pink shade (c) Real, inverted, diminished image in red shade (d) Virtual, erect, enlarged image in red shade Answer: (c) Explanation: Concave mirror always forms real and diminished image of distant object.

Question 48: A student has obtained an image of a well-illuminated distant object on a screen to determine the focal length, f 1 of the given spherical mirror. The teacher then gave him another mirror of focal length, f 2 and asked him to obtain a focussed image of the same object on the same screen. The student found that in order to focus the same object using the second mirror, he has to move the mirror away from the screen. From this observation it may be concluded that both the spherical mirrors given to the student were (select the correct option) (a ) Concave and  f 2  > f 1 (b) Concave and f 1 > f 2 (c) Convex and f 2  < f 1 (d) Convex and f 1 > f 2 Answer: (a) Explanation: Concave mirror will give the real focus and on moving the mirror away from the screen “f 2 ” is greater than f 1 .

We hope this CBSE Class 10 Science Lab Manual Focal Length of Concave Mirror and Convex Lens helps you in your preparation for CBSE Class 10 Board Examination Practical Exams. For any questions pertaining to CBSE Class 10 Science Practicals Focal Length of Concave Mirror and Convex Lens Material, feel free to leave queries in the comments section.

More Resources CBSE Class 10 Lab Manual Practical Skills:

• CBSE Class 10 Science Practical Skills
• CBSE Class 10 Maths Lab Manual
• CBSE Class 10 Math Labs with Activity

Maths NCERT Solutions

SCIENCE NCERT SOLUTIONS

Focal Length of a Concave Mirror and a Convex Lens using U-V Method

1 introduction.

• For an appropriate object distance u , find the image distance v . Measure u and v .

1.1 Concave Mirror

SVG-Viewer needed.

• The graph is hyperbola with asymptotes at u = f and v = f i.e., for the object placed at F the image is formed at infinity and for the object placed at infinity the image is formed at F.
• The values of u and v are equal at point C, which corresponds to u = v = 2 f . This point is the intersection of u - v curve and the straight line v = u . This represents centre of curvature of the mirror.

1.2 Convex Lens

• The graph is hyperbola with asymptotes at u = - f and v = f i.e., for the object placed at F the image is formed at infinity and for the object at infinity the image is formed at F.
• At the point C, the values of u and v are equal in magnitude but opposite in sign i.e., v = - u = 2 f . This point is the intersection of u - v curve and the straight line v = - u . If an object is placed at a distance 2 f from the pole then its image is formed at a distance 2 f from the pole (on the other side).

2 IIT JEE Solved Problems

• x < f
• f < x < 2 f
• x > 2 f
• 0 . 5 ± 0 . 1
• 0 . 5 ± 0 . 05
• a concave mirror of suitable focal length.
• a convex mirror of suitable focal length.
• a convex lens of focal length less than 0 . 25 m.
• a concave lens of suitable focal length.
• Convex lens
• Concave lens
• Convex mirror
• Concave mirror
• half of the image will disappear.
• complete image will be formed.
• intensity of the image will increase.
• intensity of the image will decrease.

3 Experiment Details

3.1 procedure.

• Fix the given concave mirror on the stand. Arrange the screen on the table so that the image of the distant object is obtained on it. Measure the distance between mirror and screen using a metre scale. This distance is the approximate focal length ( f ) of the mirror.
• Set the values of u ranging from 1 . 5 f to 2 . 5 f . Divide the range into a number of equal steps.
• Place the mirror in front of an illuminated object. Now, fix the mirror at the distance u (which is obtained as 1 . 5 f ).
• Place the screen on the table facing the mirror in such a way that the reflected image lies on the screen. Keeping the distance between object and mirror fixed, adjust the position of screen in order to get the clear image of the object. Remove the parallax to get accurate position of the image.
• Measure the distance between mirror and object, as well as mirror and screen. Take these values as u and v respectively. Calculate the focal length of the given concave mirror by using the relation, f = uv∕ ( u + v ).
• Repeat the experiment for different values of u (up to 2 . 5 f ) and in each time, measure v and record it in the tabular column. Calculate the focal length ( f ) of the concave mirror each time.
• Calculate the mean of all focal lengths to get the correct focal length of the given concave mirror.
• The focal length of the mirror can also be measured graphically by plotting graphs between u and v , and 1 ∕u and 1 ∕v .

3.2 Precautions

• The principal axis of the mirror should be horizontal and parallel to central line of the optical bench.
• The object should be vertical.
• Index correction for u and v should be applied.

3.3 Data Table

4 Exercise Problems

• d∕ ( m 1 - m 2 )
• d∕ ( m 1 + m 2 )
• dm 1 ∕m 2
• dm 2 ∕m 1
• md ∕ ( m + 1) 2
• md ∕ ( m + 1)
• md ∕ ( m - 1) 2
• md ∕ ( m - 1)
• ( x + y ) ∕ 2
• 36 cm
• 72 cm
• 18 cm
• 9 cm
• 4 cm
• 20 cm
• 40 cm
• 30 cm
• 60 cm
• x = +20 cm
• x = - 30 cm
• x = - 10 cm
• x = 0 cm
• d∕ 2
• d∕ 3
• d∕ 4
• virtual image is always larger in size
• real image is always smaller in size
• real image is always larger in size
• real image may be larger or smaller in size
• 40.5 cm
• -40 cm
• -45 cm
• u = - 10   cm , f = 20   cm
• u = - 20   cm , f = - 30   cm
• u = - 45   cm , f = - 10   cm
• u = - 60   cm , f = 30   cm
• must be less than 10 cm
• must be greater than 20 cm
• must not be be greater than 20 cm
• must not be less than 10 cm
• The mirror equation is one which connects u , v , and f .
• Real inverted image with same size is obtained if the object is placed on the centre of curvature of a concave mirror.
• The image formed in concave mirror is always real.
• Concave mirrors have reflecting inner surface.

5 Do it Yourself

5.1 focal length of a concave mirror.

• Firstly, find the approximate focal length ( f ) of a concave mirror. You can do this by focusing a distant object like sun. Fix mirror vertically on a V-stand. Draw a long straight line on a table and place the mirror stand on it. The pole of the mirror should be exactly above the line.
• Light a candle and place it on one end of the line. The flame of the candle should be at the same height as the pole of the mirror.
• Fix the screen on its stand. The screen should be vertical. Place the screen between the candle and mirror.
• Analyse the nature of the image by moving the screen and/or mirror.
• For three different values of u , find the value of v . Calculate f by substituting in mirror formula.

5.2 Focal Length of the Convex Lens

• Firstly, find the approximate focal length ( f ) of the convex lens. Then fix it vertically on a V-stand. Draw a long straight line on a table and place the lens in the middle. The pole of the lens should be exactly above the line.
• Light a candle and place it on one end of the line. The flame of the candle should be at the same height as the pole of the lens.
• Fix the screen on its stand. The screen should be vertical. Place the screen on other side of the lens.
• Analyse the nature of the image by moving the screen and/or lens.
• For three different values of u , find the value of v . Calculate f by substituting in the lens formula.

6 More…

6.1 plane mirror method.

• virtual and at a distance of 16 cm from the mirror.
• real and at a distance of 16 cm from the mirror.
• virtual and at a distance of 20 cm from the mirror.
• real and at a distance of 20 cm from the mirror.

6.2 Displacement Method or Two Position Method

6.3 the minimum distance method.

[1]     Focal length of a concave mirror by u-v method. https://goo.gl/PqDHRp . Good webpage at www.learncbse.in.

[2]     Focal length of a convex lens by u-v method. https://goo.gl/PT39i1 . Good webpage at www.learncbse.in.

[3]     Focal length of concave mirror by u-v method. https://goo.gl/RqsX3D . Amrita Olabs Webpage.

[4]     Focal length of concave mirror by u-v method. https://youtu.be/j8N1Z6338UQ . Amrita OLabs YouTube Video.

[5]     Focal length of the concave mirror. https://youtu.be/5DbdWFAs8EI . Good YouTube Video from Edunovas.

[6]     Focal length of the convex lens. https://youtu.be/f0bi0yl7uZU . Good YouTube Video from Edunovas.

[7]     The measurement of the focal length of a lens. https://goo.gl/Rxy3gr . This webpage gives various methods to find focal length of a lens.

[8]     NCERT book to find the focal length of a convex lens. http://ncert.nic.in/ncerts/l/lelm305.pdf . Download PDF from here.

[9]     HC Verma. Concepts of Physics , volume Part 1. Bharati Bhawan, 1992.

To Measure the Focal Length of a Concave Mirror

When an object is placed in front of a concave mirror (outside the focal point), a real image is formed. The image can be seen on a screen that is moved to the position of the image. In this experiment a slit at the front of a ray box is the object. The ray box and the screen can be moved using sliders. The object distance (u) and image distance (v) is measured each time an image is found on the screen. The focal length (f), which is multiples of 5, can then be calculated using the formula: 1/f = 1/u + 1/v Note: When you move the ray box inside the focal point you do not get a real image. It is virtual and behind the mirror. Not shown here.

• Using the left hand slider, drag the ray box towards the mirror.
• Drag the screen to the point where the reflected rays meet to form the sharpest image.
• Press "Measure u" and record its value.
• Press "Measure v" and record its value.
• Use the formula: 1/u + 1/v = 1/f to calculate f.
• Repeat steps 1 to 5 until you have at least six sets of readings.
• Press "New f value" to get another random value and repeat steps 1 to 6.
• Avoid parallax errors (eye directly in front of metre stick) when measuring u and v.
• Measure from the centre of the back of the mirror (the point where reflection occurs) in all cases.

25.7 Image Formation by Mirrors

Learning objectives.

By the end of this section, you will be able to:

• Illustrate image formation in a flat mirror.
• Explain with ray diagrams the formation of an image using spherical mirrors.
• Determine focal length and magnification given radius of curvature, distance of object and image.

We only have to look as far as the nearest bathroom to find an example of an image formed by a mirror. Images in flat mirrors are the same size as the object and are located behind the mirror. Like lenses, mirrors can form a variety of images. For example, dental mirrors may produce a magnified image, just as makeup mirrors do. Security mirrors in shops, on the other hand, form images that are smaller than the object. We will use the law of reflection to understand how mirrors form images, and we will find that mirror images are analogous to those formed by lenses.

Figure 25.38 helps illustrate how a flat mirror forms an image. Two rays are shown emerging from the same point, striking the mirror, and being reflected into the observer’s eye. The rays can diverge slightly, and both still get into the eye. If the rays are extrapolated backward, they seem to originate from a common point behind the mirror, locating the image. (The paths of the reflected rays into the eye are the same as if they had come directly from that point behind the mirror.) Using the law of reflection—the angle of reflection equals the angle of incidence—we can see that the image and object are the same distance from the mirror. This is a virtual image, since it cannot be projected—the rays only appear to originate from a common point behind the mirror. Obviously, if you walk behind the mirror, you cannot see the image, since the rays do not go there. But in front of the mirror, the rays behave exactly as if they had come from behind the mirror, so that is where the image is situated.

Now let us consider the focal length of a mirror—for example, the concave spherical mirrors in Figure 25.39 . Rays of light that strike the surface follow the law of reflection. For a mirror that is large compared with its radius of curvature, as in Figure 25.39 (a), we see that the reflected rays do not cross at the same point, and the mirror does not have a well-defined focal point. If the mirror had the shape of a parabola, the rays would all cross at a single point, and the mirror would have a well-defined focal point. But parabolic mirrors are much more expensive to make than spherical mirrors. The solution is to use a mirror that is small compared with its radius of curvature, as shown in Figure 25.39 (b). (This is the mirror equivalent of the thin lens approximation.) To a very good approximation, this mirror has a well-defined focal point at F that is the focal distance f f from the center of the mirror. The focal length f f of a concave mirror is positive, since it is a converging mirror.

Just as for lenses, the shorter the focal length, the more powerful the mirror; thus, P = 1 / f P = 1 / f for a mirror, too. A more strongly curved mirror has a shorter focal length and a greater power. Using the law of reflection and some simple trigonometry, it can be shown that the focal length is half the radius of curvature, or

where R R is the radius of curvature of a spherical mirror. The smaller the radius of curvature, the smaller the focal length and, thus, the more powerful the mirror.

The convex mirror shown in Figure 25.40 also has a focal point. Parallel rays of light reflected from the mirror seem to originate from the point F at the focal distance f f behind the mirror. The focal length and power of a convex mirror are negative, since it is a diverging mirror.

Ray tracing is as useful for mirrors as for lenses. The rules for ray tracing for mirrors are based on the illustrations just discussed:

• A ray approaching a concave converging mirror parallel to its axis is reflected through the focal point F of the mirror on the same side. (See rays 1 and 3 in Figure 25.39 (b).)
• A ray approaching a convex diverging mirror parallel to its axis is reflected so that it seems to come from the focal point F behind the mirror. (See rays 1 and 3 in Figure 25.40 .)
• Any ray striking the center of a mirror is followed by applying the law of reflection; it makes the same angle with the axis when leaving as when approaching. (See ray 2 in Figure 25.41 .)
• A ray approaching a concave converging mirror through its focal point is reflected parallel to its axis. (The reverse of rays 1 and 3 in Figure 25.39 .)
• A ray approaching a convex diverging mirror by heading toward its focal point on the opposite side is reflected parallel to the axis. (The reverse of rays 1 and 3 in Figure 25.40 .)

We will use ray tracing to illustrate how images are formed by mirrors, and we can use ray tracing quantitatively to obtain numerical information. But since we assume each mirror is small compared with its radius of curvature, we can use the thin lens equations for mirrors just as we did for lenses.

Consider the situation shown in Figure 25.41 , concave spherical mirror reflection, in which an object is placed farther from a concave (converging) mirror than its focal length. That is, f f is positive and d o d o > f f , so that we may expect an image similar to the case 1 real image formed by a converging lens. Ray tracing in Figure 25.41 shows that the rays from a common point on the object all cross at a point on the same side of the mirror as the object. Thus a real image can be projected onto a screen placed at this location. The image distance is positive, and the image is inverted, so its magnification is negative. This is a case 1 image for mirrors . It differs from the case 1 image for lenses only in that the image is on the same side of the mirror as the object. It is otherwise identical.

Example 25.9

A concave reflector.

Electric room heaters use a concave mirror to reflect infrared (IR) radiation from hot coils. Note that IR follows the same law of reflection as visible light. Given that the mirror has a radius of curvature of 50.0 cm and produces an image of the coils 3.00 m away from the mirror, where are the coils?

Strategy and Concept

We are given that the concave mirror projects a real image of the coils at an image distance d i = 3.00 m d i = 3.00 m . The coils are the object, and we are asked to find their location—that is, to find the object distance d o d o . We are also given the radius of curvature of the mirror, so that its focal length is f = R / 2 = 25.0 cm f = R / 2 = 25.0 cm (positive since the mirror is concave or converging). Assuming the mirror is small compared with its radius of curvature, we can use the thin lens equations, to solve this problem.

Since d i d i and f f are known, thin lens equation can be used to find d o d o :

Rearranging to isolate d o d o gives

Entering known quantities gives a value for 1/ d o 1/ d o :

This must be inverted to find d o d o :

Note that the object (the filament) is farther from the mirror than the mirror’s focal length. This is a case 1 image ( d o > f d o > f and f f positive), consistent with the fact that a real image is formed. You will get the most concentrated thermal energy directly in front of the mirror and 3.00 m away from it. Generally, this is not desirable, since it could cause burns. Usually, you want the rays to emerge parallel, and this is accomplished by having the filament at the focal point of the mirror.

Note that the filament here is not much farther from the mirror than its focal length and that the image produced is considerably farther away. This is exactly analogous to a slide projector. Placing a slide only slightly farther away from the projector lens than its focal length produces an image significantly farther away. As the object gets closer to the focal distance, the image gets farther away. In fact, as the object distance approaches the focal length, the image distance approaches infinity and the rays are sent out parallel to one another.

Example 25.10

Solar electric generating system.

One of the solar technologies used today for generating electricity is a device (called a parabolic trough or concentrating collector) that concentrates the sunlight onto a blackened pipe that contains a fluid. This heated fluid is pumped to a heat exchanger, where its heat energy is transferred to another system that is used to generate steam—and so generate electricity through a conventional steam cycle. Figure 25.42 shows such a working system in southern California. Concave mirrors are used to concentrate the sunlight onto the pipe. The mirror has the approximate shape of a section of a cylinder. For the problem, assume that the mirror is exactly one-quarter of a full cylinder.

• If we wish to place the fluid-carrying pipe 40.0 cm from the concave mirror at the mirror’s focal point, what will be the radius of curvature of the mirror?
• Per meter of pipe, what will be the amount of sunlight concentrated onto the pipe, assuming the insolation (incident solar radiation) is 0.900 k W/m 2 0.900 k W/m 2 ?
• If the fluid-carrying pipe has a 2.00-cm diameter, what will be the temperature increase of the fluid per meter of pipe over a period of one minute? Assume all the solar radiation incident on the reflector is absorbed by the pipe, and that the fluid is mineral oil.

To solve an Integrated Concept Problem we must first identify the physical principles involved. Part (a) is related to the current topic. Part (b) involves a little math, primarily geometry. Part (c) requires an understanding of heat and density.

Solution to (a)

To a good approximation for a concave or semi-spherical surface, the point where the parallel rays from the sun converge will be at the focal point, so R = 2 f = 80.0 cm R = 2 f = 80.0 cm .

Solution to (b)

The insolation is 900 W /m 2 900 W /m 2 . We must find the cross-sectional area A A of the concave mirror, since the power delivered is 900 W /m 2 × A 900 W /m 2 × A . The mirror in this case is a quarter-section of a cylinder, so the area for a length L L of the mirror is A = 1 4 (2 πR )L A = 1 4 (2 πR )L . The area for a length of 1.00 m is then

The insolation on the 1.00-m length of pipe is then

Solution to (c)

The increase in temperature is given by Q = mc Δ T Q = mc Δ T . The mass m m of the mineral oil in the one-meter section of pipe is

Therefore, the increase in temperature in one minute is

Discussion for (c)

An array of such pipes in the California desert can provide a thermal output of 250 MW on a sunny day, with fluids reaching temperatures as high as 400º C 400º C . We are considering only one meter of pipe here, and ignoring heat losses along the pipe.

What happens if an object is closer to a concave mirror than its focal length? This is analogous to a case 2 image for lenses ( d o < f d o < f and f f positive), which is a magnifier. In fact, this is how makeup mirrors act as magnifiers. Figure 25.43 (a) uses ray tracing to locate the image of an object placed close to a concave mirror. Rays from a common point on the object are reflected in such a manner that they appear to be coming from behind the mirror, meaning that the image is virtual and cannot be projected. As with a magnifying glass, the image is upright and larger than the object. This is a case 2 image for mirrors and is exactly analogous to that for lenses.

All three rays appear to originate from the same point after being reflected, locating the upright virtual image behind the mirror and showing it to be larger than the object. (b) Makeup mirrors are perhaps the most common use of a concave mirror to produce a larger, upright image.

A convex mirror is a diverging mirror ( f f is negative) and forms only one type of image. It is a case 3 image—one that is upright and smaller than the object, just as for diverging lenses. Figure 25.44 (a) uses ray tracing to illustrate the location and size of the case 3 image for mirrors. Since the image is behind the mirror, it cannot be projected and is thus a virtual image. It is also seen to be smaller than the object.

Example 25.11

Image in a convex mirror.

A keratometer is a device used to measure the curvature of the cornea, particularly for fitting contact lenses. Light is reflected from the cornea, which acts like a convex mirror, and the keratometer measures the magnification of the image. The smaller the magnification, the smaller the radius of curvature of the cornea. If the light source is 12.0 cm from the cornea and the image’s magnification is 0.0320, what is the cornea’s radius of curvature?

If we can find the focal length of the convex mirror formed by the cornea, we can find its radius of curvature (the radius of curvature is twice the focal length of a spherical mirror). We are given that the object distance is d o = 12.0 cm d o = 12.0 cm and that m = 0.0320 m = 0.0320 . We first solve for the image distance d i d i , and then for f f .

m = –d i / d o m = –d i / d o . Solving this expression for d i d i gives

Entering known values yields

Substituting known values,

This must be inverted to find f f :

The radius of curvature is twice the focal length, so that

The radius of curvature found here is reasonable for a cornea. The distance from cornea to retina in an adult eye is about 2.0 cm. In practice, many corneas are not spherical, complicating the job of fitting contact lenses. Note that the image distance here is negative, consistent with the fact that the image is behind the mirror, where it cannot be projected. In this section’s Problems and Exercises, you will show that for a fixed object distance, the smaller the radius of curvature, the smaller the magnification.

The three types of images formed by mirrors (cases 1, 2, and 3) are exactly analogous to those formed by lenses, as summarized in the table at the end of Image Formation by Lenses . It is easiest to concentrate on only three types of images—then remember that concave mirrors act like convex lenses, whereas convex mirrors act like concave lenses.

Take-Home Experiment: Concave Mirrors Close to Home

Find a flashlight and identify the curved mirror used in it. Find another flashlight and shine the first flashlight onto the second one, which is turned off. Estimate the focal length of the mirror. You might try shining a flashlight on the curved mirror behind the headlight of a car, keeping the headlight switched off, and determine its focal length.

Problem-Solving Strategy for Mirrors

Step 1. Examine the situation to determine that image formation by a mirror is involved.

Step 2. Refer to the Problem-Solving Strategies for Lenses . The same strategies are valid for mirrors as for lenses with one qualification—use the ray tracing rules for mirrors listed earlier in this section.

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• Authors: Paul Peter Urone, Roger Hinrichs
• Publisher/website: OpenStax
• Book title: College Physics 2e
• Publication date: Jul 13, 2022
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• Determination of the focal length of Concave mirror by obtaining the image of a distant object

To determine the focal length of a concave mirror by obtaining the image of a distant object.

Apparatus required.

• Concave mirror
• A meter scale
• A mirror holder
• A screen holder
• A concave mirror is defined as the spherical mirror whose reflecting surface is curved inwards and follows laws of reflection of light.
• When the object is at infinity, then real, inverted and highly diminished image is formed at focus.
• The light rays coming from a distant object can be considered to be parallel to each other.
• If the image formed is real, inverted and very small in size, then the parallel rays of light meet the point in the front of the mirror.

• Fix a concave mirror in the mirror holder and place it on the table near an open window. Turn the face of mirror towards a distant object (suppose a tree).
• Place the screen, fitted to a stand, in front of the concave mirror.
• Adjust the distance of screen, so that the image of the distant object is formed on it as given in the figure below. We can infer from the figure that a clear and bright image could be obtained if the distant object (a tree), is illuminated with sunlight and the screen is placed in the shade. A bright image of the Sun could also be obtained, if the sunlight is made to fall directly on the concave mirror.
• When a sharp image of distant object is obtained, then mark the position of the Centre of the stand holding the mirror and the screen as (a) and (b), respectively (see Fig 3).
• Measure the horizontal distance between the Centre of the concave mirror and the screen with the help of a measuring scale.
• Repeat the experiment two more times by obtaining the images of two different distant objects and measure the distance between the concave mirror and the screen in each case. Record them in the observation table.
• Find the mean value of the focal length for all the observations for different objects.

Observations

Calculation

The approximate value of focal length of the given concave mirror = 29.93 cm.

Precautions

• Concave mirror should be placed near an open window through which sufficient sunlight enters, with its polished surface facing the distant object.
• There should not be any obstacle in the path of rays of light incident on the concave mirror.
• In order to obtain a sharp and clear image of the distant object on the wall/ground, it must be ensured that the object is well illuminated, so that amount of light incident on the concave mirror is sufficient to produce a well illuminated and distinct image.
• The measuring scale should be parallel to the base of both the stands.
• The mirror holder along with the mirror should be kept perpendicular to the measuring scale for precise measurements.

Class 10 Physics Practicals

• To study the dependence of current on the potential difference with graph
• Determination of equivalent resistance of two resistors when connected in series
• Determination of equivalent resistance of two resistors when connected in parallel
• Determination of the focal length of Convex lens by obtaining the image of a distant object
• Tracing the path of a ray of light passing through a rectangular glass slab for different angles of incidence
• Tracing the path of the rays of light through a glass prism

Class 10 Chemistry Practicals

• Finding the pH of the samples by using pH paper/universal indicator
• Studying the properties of acids and bases (HCl & NaOH) on the basis of their reaction
• Performing and observing the reactions and classifying them into: i. Combination reaction, ii. Decomposition reaction, iii. Displacement reaction and iv. Double displacement reaction
• Observing the action of Zn, Fe, Cu and Al metals on the salt solutions
• Studying the properties of acetic acid (ethanoic acid)
• Studying saponification reaction for preparation of soap
• Studying the comparative cleaning capacity of a sample of soap in soft and hard water

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Focal length of a concave mirror.

Use a light source, concave mirror, and half screen accessory on an optics bench to measure the focal length of the concave mirror.

Grade Level: College

Subject: Physics

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A complete optics bench that includes all the components required to do introductory optics experiments.

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In an experiment to find the focal length of a concave mirror, a graph is drawn between the magnitudes of $u$ and $v$. The graph looks like: A) B) C) D)

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In an experiment of find the focal length of a concave mirror a graph is drawn between the magnitudes of u and v. The graph looks like [AIIMS 2003]

The correct option is C