spherometer experiment class 11

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To determine the radius of curvature of a given spherical surface by a spherometer

To determine the radius of curvature of a given spherical surface by a spherometer.

Apparatus and material required

A spherometer, a spherical surface such as a watch glass or a convex mirror and a plane glass plate of about 6 cm x 6 cm size.

Description of Apparatus

A spherometer consists of a metallic triangular frame F supported on three legs of equal length A, B and C (Fig. E 3.1). The lower tips of the legs form three corners of an equilateral triangle ABC and lie on the periphery of a base circle of known radius, r. The spherometer also consists of a central leg OS (an accurately cut screw), which can be raised or lowered through a threaded hole V (nut) at the centre of the frame F. The lower tip of the central screw, when lowered to the plane (formed by the tips of legs A, B and C) touches the centre of triangle ABC. The central screw also carries a circular disc D at its top having a circular scale divided into 100 or 200 equal parts. A small vertical scale P marked in millimetres or half-millimetres, called main scale is also fixed parallel to the central screw, at one end of the frame F. This scale P is kept very close to the rim of disc D but it does not touch the disc D. This scale reads the vertical distance which the central leg moves through the hole V. This scale is also known as pitch scale.

Terms and Definitions

Pitch: It is the vertical distance moved by the central screw in one complete rotation of the circular disc scale. Commonly used spherometers in school laboratories have graduations in millimetres on pitch scale and may have100 equal divisions on circular disc scale. In one rotation of the circular scale, the central screw advances or recedes by 1 mm. Thus, the pitch of the screw is 1 mm.

Least Count: Least count of a spherometer is the distance moved by the spherometer screw when it is turned through one division on the circular scale, i.e.,

Least count of the spherometer =Pitchof thespherometerscrew /Numberof divisions on the circular scale

The least count of commonly used spherometers is 0.01 mm. However, some spherometers have least count as small as 0.005 mm or 0.001 mm.

Formula for The Radius of Curvature of A Spherical Surface

Let the circle AOBXZY (Fig. E 3.2) represent the vertical section of sphere of radius R with E as its centre (The given spherical surface is a part of this sphere). Length OZ is the diameter (= 2R ) of this vertical section, which bisects the chord AB. Points A and B are the positions of the two spherometer legs on the given spherical surface. The position of the third spherometer leg is not shown in Fig. E 3.2. The point O is the point of contact of the tip of central screw with the spherical surface. Fig. E 3.3 shows the base circle and equilateral triangle ABC formed by the tips of the three spherometer legs. From this figure, it can be noted that the point M is not only the mid point of line AB but it is the centre of base circle and centre of the equilateral triangle ABC formed by the lower tips of the legs of the spherometer (Fig. E 3.1). In Fig. E 3.2 the distance OM is the height of central screw above the plane of the circular section ABC when its lower

tip just touches the spherical surface. This distance OM is also called sagitta. Let this be h. It is known that if two chords of a circle, such as AB and OZ, intersect at a point M then the areas of the rectangles described by the two parts of chords are equal. Then

AM.MB = OM.MZ

(AM) 2 = OM (OZ - OM) as AM = MB

Let EZ (= OZ/2) = R, the radius of curvature of the given spherical surface and AM = r, the radius of base circle of the spherometer.

r 2 = h (2R - h)

Thus, R = r 2 /2h + h/2

Now, let l be the distance between any two legs of the spherometer or the side of the equilateral triangle ABC (Fig. E 3.3), then from geometry we have

Thus, r = 1/√ 3 , the radius of curvature (R) of the given spherical surface can be given by

R= ι 2 /6h + h/2

• Note the value of one division on pitch scale of the given spherometer.
• Note the number of divisions on circular scale.
• Determine the pitch and least count (L.C.) of the spherometer. Place the given flat glass plate on a horizontal plane and keep the spherometer on it so that its three legs rest on the plate.
• Place the spherometer on a sheet of paper (or on a page in practical note book) and press it lightly and take the impressions of the tips of its three legs. Join the three impressions to make an equilateral triangle ABC and measure all the sides of Δ ABC. Calculate the mean distance between two spherometer legs, l.
• In the determination of radius of curvature R of the given spherical surface, the term ι 2 is used (see formula used). Therefore, great care must be taken in the measurement of length, ι.
• Place the given spherical surface on the plane glass plate and then place the spherometer on it by raising or lowering the central screw sufficiently upwards or downwards so that the three spherometer legs may rest on the spherical surface (Fig. E 3.4).
• Rotate the central screw till it gently touches the spherical surface. To be sure that the screw touches the surface one can observe its image formed due to reflection from the surface beneath it.
• Take the spherometer reading h1 by taking the reading of the pitch scale. Also read the divisions of the circular scale that is in line with the pitch scale. Record the readings in Table E 3.1.
• Remove the spherical surface and place the spherometer on plane glass plate. Turn the central screw till its tip gently touches the glass plate. Take the spherometer reading h 2 and record it in Table E 3.1. The difference between h 1 and h 2 is equal to the value of sagitta (h).
• Repeat steps (5) to (8) three more times by rotating the spherical surface leaving its centre undisturbed. Find the mean value of h.

Observations

A. Pitch of the screw:

• Value of smallest division on the vertical pitch scale = ... mm
• Distance q moved by the screw for p complete rotations of the circular disc = ... mm
• Pitch of the screw ( = q / p ) = ... mm

Least Count (L.C.) of the spherometer:

• Total no. of divisions on the circular scale (N ) = ...
• Least count (L.C.) of the spherometer
• = Pitchof thespherometerscrew /Numberof divisionsonthecircular scale
• L.C. = Pitchof thescrew /N = ... cm

Determination of length l (from equilateral triangle ABC)

• Distance AB = ... cm
• Distance BC = ... cm
• Distance CA = ... cm
• Mean ι = AB + BC+ CA /3= ... cm

Table E 3.1 Measurement of sagitta h

Mean h = ... cm

Calculation

Using the values of l and h, calculate the radius of curvature R from the formula:

R = ι 2 /6h + h/2;

the term h/2 may safely be dropped in case of surfaces of large radii of curvature (In this situation error in ι 2 /6h is of the order of h/2.)

The radius of curvature R of the given spherical surface is ... cm.

Precautions

• The screw may have friction.
• Spherometer may have backlash error.

Sources of Error

• Parallax error while reading the pitch scale corresponding to the level of the circular scale
• Backlash error of the spherometer.
• on-uniformity of the divisions in the circular scale.
• While setting the spherometer, screw may or may not be touching the horizontal plane surface or the spherical surface.

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• 5 To determine the radius of curvature of a given spherical surface by a spherometer
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Measuring with Spherometer: A Virtual Lab Experiment

What is the Radius of the Curvature of the Spherical Surface? 

Spherical surfaces are the part of the sphere which is used to form the image as per the requirement of an object using the principle of reflection of light. There are two types of spherical surfaces: convex and concave.

The linear distance between the pole and centre of curvature is called the radius of curvature. The centre of the spherical surface is called the pole, whereas the centre of the sphere (from which the spherical surface is cut ) is called the centre of curvature. When the radius of curvature becomes infinite, the spherical mirror behaves as a plane mirror. The radius of curvature lies on the principal axis of the spherical surface.

Diagram of Spherometer

Given below is the labeled diagram of a Spherometer.

How to read Spherometer?

The following is the procedure for using a spherometer:

• First, place the instrument on the perfect plane surface, so the central leg is screwed down slowly until it touches the surface. When the central leg touches the surface, the instrument rounds on the central leg as the centre.
• Remove the spherometer from the surface to take the reading from the micrometre screw. If the instrument works fine, the reading should be 0-0. However, there is always a slight error in the instrument, which could be either a positive or negative error.
• Take the instrument off the plane and draw the central leg back.
• Let’s consider measuring the sphere’s radius from the convex side.
• Now read the scale and screw-head. If the reading is 2.0 and 0.155, then the total reading is 2.155.
• If the reading is below the zero lines, then the reading should be added to the zero error. If the reading is above the zero lines, then the reading should be subtracted from the zero error.
• To measure the length between the two legs, place the instrument on the plain card and measure the length using a meter scale.
• The radius of curvature can be calculated using the following equation:

What is the Least Count of Spherometer?

The least count (L.C) can be calculated using the relation,

Pitch of a Spherometer: The pitch is defined as the distance covered by the circular disc in one complete rotation along the main scale. Therefore, the pitch of a spherometer is given as 1 mm = 0.1 cm.

Number of circular divisions = 100

What is Zero Error in Spherometer?

A zero error is an error in your readings determined when the true value of what you’re measuring is zero, but the instrument reads a non-zero value. 

A spherometer does not have a zero error because the result obtained is by taking the difference between the final and initial reading.

Applications of Spherometer

The primary application of a spherometer is to measure the radii of curvature of spherical surfaces such as optical lenses, spherical mirrors, and balls. These small, high-precision optical test instruments are also used to measure the thickness of microscope slides or the depth of slide depressions.

Solved Examples for Spherometer

Ex-1. A student measures the height h of a convex mirror using a spherometer. The legs of the spherometer are 4 cm apart, and there are ten divisions per cm on its linear scale, and the circular scale has 50 divisions. The student takes two as linear scale division and 40 as circular scale division. What is the radius of curvature of the convex mirror?   

The values of I and h are 4.0 cm and 0.065 cm, respectively, where ‘I’ is measured by a meter scale and h by a spherometer. Find the relative error in the measurement of R.

Spherometer Experiment

Experiment Title – Use of Spherometer to Find Radius of Curvature  

Experiment Description – A spherometer is a precision instrument that measures very small lengths. Let’s determine the radius of curvature of a given spherical surface using a spherometer.

Aim of Experiment – To determine the radius of curvature of a given spherical surface by a spherometer.

Material Required – A spherometer, a convex glass surface, a plane glass plate, a pencil, a measuring scale, a paper sheet and a small piece of paper.

Procedure – 

• Observe the given spherometer and note the value of one division of its pitch scale.
• Observe the circular scale and note the number of divisions on it.
• Determine the least count (L.C.) and pitch of the spherometer. Place the given flat glass plate on a horizontal plane and the spherometer on it so that its three legs rest on the plate.
• Take a sheet of paper, place the spherometer on it, and press it gently to take the impressions of the tips of the three legs. Make an equilateral triangle ABC by joining the three impressions and measuring all the sides of the ΔABC. Determine the mean distance between two spherometer legs, l.

Take great care in measuring the length l as the term l 2 is used to determine curvature R of the given spherical surface.

• Place the given spherical surface on the plane glass plate and then place the spherometer on it by raising the central screw sufficiently upwards so that the three legs of the spherometer rest on the spherical surface, as shown in the figure below. 

• Rotate the central screw till its lower tip gently touches the spherical surface. Observe the image of the screw formed due to the reflection from the surface below to make sure that the screw touches the surface.
• Observe the reading of the pitch scale and the divisions of the circular scale that is in line with the pitch scale to take the spherometer reading h 1 . Record the observations in the observation table. 
• Remove the spherical surface and place the spherometer on the plane glass plate. Turn the central screw till its lower tip gently touches the glass plate. Again, take the spherometer reading h 2 and record it in the observation table. The difference between h 1 and h 2 equals the value of sagitta (h).
• Repeat steps (5) to (8) three more times by rotating the spherical surface without disturbing its centre. Find the mean value of h.

Precautions – 

• The screw of the spherometer may have friction. 
• The spherometer may have a backlash error. 

FAQs on Spherometer

It works on the principle of a micrometre screw.

A spherometer has three legs so that it forms an equilateral triangle. The three legs of the spherometer are used for measuring positively and negatively curved surfaces.

The pitch is the distance covered by the circular disc in one complete rotation along the main scale. Therefore, the pitch of a spherometer is given as 1 mm = 0.1 cm.

The accuracy of the spherometer can be increased by decreasing the pitch or increasing the number of divisions of the circular scale. The smaller the least count, the more the accuracy of an instrument and vice versa.

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Physics Practical Class 11 Lab Manual

• General Introduction
• To measure diameter of a small spherical/cylindrical body using Vernier Callipers.
• To measure the dimensions of a given regular body of known mass using a Vernier Callipers and hence find its density.
• To measure internal diameter and depth of a given beaker/calorimeter using a Vernier Callipers and hence find its volume.
• To measure diameter of a given wire using screw gauge.
• To measure thickness of a given sheet using screw gauge.
• To determine volume of an irregular lamina using screw gauge.
• To determine radius of curvature of a given spherical surface by a spherometer.
• To determine the mass of two different objects using a beam balance.
• Measurement of Time
• To find the weight of a given body using parallelogram law of vectors.
• Using a simple pendulum, plot its L-T 2 graph and use it to find the effective length of second’s pendulum.
• To study variation of time period of a simple pendulum r of a given length by taking bobs of same size but different masses and interpret the result.
• To study the relationship between force of limiting friction and normal reaction and to find the co-efficient of friction between a block and a horizontal surface.
• To find the downward force, along an inclined plane, acting on a roller due to gravitational pull of the earth and study its relationship with the angle of inclination θ by plotting graph between force and sin θ.
• To make a paper scale of given least count, e.g., 0.2 cm, 0.5 cm.
• To determine mass of a given body using a metre scale by principle of moments.
• To plot a graph for a given set of data, with proper choice of scales and error bars.
• To measure the force of limiting friction for rolling of roller on a horizontal plane.
• To study the variation in range of a projectile with angle of projection.
• To study the conservation of energy of a ball rolling down on an inclined plane (using a double inclined plane).
• To study dissipation of energy of a simple pendulum by plotting a graph between square of amplitude and time.
• To determine Young’s modulus of elasticity of the material of a given wire.
• To find the force constant of a helical spring by plotting a graph between load and extension.
• To study the variation in volume with pressure for a sample of air at constant temperature by plotting graphs between P and V, and between P and 1/V.
• To determine the surface tension of water by capillary rise method.
• To determine the coefficient of viscosity of a given viscous liquid by measuring terminal velocity of a given spherical body.
• Thermal Expansion of Solids
• Thermal Expansion of Liquids
• To study the relationship between the temperature of a hot body and time by plotting a cooling curve.
• To determine specific heat capacity of a given solid by method of mixtures.
• Wave Motion and Velocity of Waves
• To study the relation between frequency and length of a given wire under constant tension using sonometer.
• To study the relation between the length of a given wire and tension for constant frequency using sonometer.
• To find the speed of sound in air at room temperature using a resonance tube by two resonance positions.
• To observe change of state and plot a cooling curve for molten wax.
• To observe and explain the effect of heating on a bi-metallic strip.
• To note the change in level of liquid in a container on heating and interpret the observations.
• To study the effect of detergent on surface tension of water by observing capillary rise.
• To study the factors affecting the rate of loss of heat of a liquid.
• To study the effect of load on depression of a suitably clamped metre scale loaded at (i) its end (ii) in the middle.
• To observe the decrease in pressure with increase in velocity of a fluid.

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CBSE Class 11 Lab Manual for Chapter 2 8 To Determine Radius of Curvature of a Given Spherical surface by a Spherometer PDF Download

CBSE Class 11 Lab Manual Chapter 2 8 To Determine Radius of Curvature of a Given Spherical surface by a Spherometer Download here in pdf format. These Lab Manual may be freely downloadable and used as a reference book. Learning does not mean only gaining knowledge about facts and principles rather it is a path which is informed by scientific truths, verified experimentally. Keeping these facts in mind, CBSE Class 11 Lab Manual for Chapter 2 8 To Determine Radius of Curvature of a Given Spherical surface by a Spherometer have been planned, evaluated under subject Improvement Activities. Check our CBSE Class 11 Lab Manual for Chapter 2 8 To Determine Radius of Curvature of a Given Spherical surface by a Spherometer. We are grateful to the teachers for their constant support provided in the preparation of this CBSE Class 11 Lab Manual.

CBSE Class 11 Lab Manual for Chapter 2 8 To Determine Radius of Curvature of a Given Spherical surface by a Spherometer

The laboratory is important for making the study complete, especially for a subject like Science and Maths. CBSE has included the practicals in secondary class intending to make students familiarised with the basic tools and techniques used in the labs. With the help of this, they can successfully perform the experiments listed in the CBSE Class 11 Lab Manual.

CBSE Class 11 Lab Manual for Chapter 2 8 To Determine Radius of Curvature of a Given Spherical surface by a Spherometer Features:

• Basic Concept of Experiments
• Before performing the experiments the basic concept section of every experiment helps the students in know the aim of the experiment and to achieve the result with the minimum mistake
• Lab Experiments with Interactive session and NCERT Lab Manual Questions 
• Completely solved CBSE Class 11 Lab Manual Questions are provided.
• Practical Based Questions
• PBQs based on every experiment with their answers, covering Previous Years’ Questions, are provided experiments for complete coverage of concepts Web support

By performing the experiments, students will know the concept in a better way as they can now view the changes happening in front of their eyes. Their basics will become solid as they will learn by doing things. By doing this activity they will also get generated their interest in the subject. Students will develop questioning skills and start studying from a scientific perspective. Here we have given all the necessary details that a Chapter 2 8 To Determine Radius of Curvature of a Given Spherical surface by a Spherometer student should know about CBSE Class 11 Lab Manual. From CBSE Science practical to Lab manual, project work, important questions and CBSE lab kit manual, all the information is given in the elaborated form further in this page for Chapter 2 8 To Determine Radius of Curvature of a Given Spherical surface by a Spherometer students.

Benefit of the CBSE Class 11 Lab Manual for Chapter 2 8 To Determine Radius of Curvature of a Given Spherical surface by a Spherometer:

• Basic concepts of every experiment have been covered for better understanding. The matter is presented in the simple and lucid language under main-headings and sub-headings.
• Detailed observation tables and graphical design of experiments are provided wherever it is necessary.
• Diagrams are well-labelled and neatly drawn.
• CBSE Class 11 Lab Manual Questions with their answers
• Multiple Choice Questions (MCQs) are completely solved with the scoring key giving the explanation of every answer
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Spherometer experiment for class 11 ENGINEERING Physics Practical

This experiment on spherometer is for engineering physics and class 11 physics practical. It is included with spherometer least count, formula for radius of curvature of spherometer, observation table for determination of radius of curvature and important viva questions on this practical.

To determine the radius of curvature of a convex/concave mirror/surface using a spherometer.

Spherometer is used to measure the thickness or the radius of curvature of a curved surface. The radius of a spherometer is R=\frac{l^{2}}{6h}+\frac{h}{2} Where l is the distance between any two legs of the spherometer and h is the perpendicular distance between the legs and screw when it is above the spherical surface

• A spherometer
• A convex/concave mirror/surface
• A plane glass plate
• A plane paper
• Raise the screw of the spherometer and press on to the practical notebook to get the marks of the three legs of the spherometer.
• Name the marks as A, B and C. Join AB, BC and CA and measure the distances. Take the mean of these distances to calculate the value of ‘l’.
• Now measure the screw pitch. Observe the linear scale moves for one complete rotation of the circular scale. Calculate least count by dividing screw pitch to total number of circular scale divisions.
• Now place the convex surface onto the glass plate. Then place the spherometer on the surface of the convex surface or mirror.

5. Read the circular scale reading when the screw and all three legs touch the convex surface. Make sure that all legs and screw touch the surface by passing a plane paper to the screw head and three legs. 6. Now remove the convex surface and place the spherometer above the plane glass sheet. 7. Count the total number of complete rotations when the spherometer screw touch the glass surface. Also take the reading of circular scale.

Distance between the two legs of the spherometer

A, B and C are legs of the spherometer. The average distance between the two legs are AB = _____ cm BC = _____ cm CA= _____ cm Mean value of length l=\frac{AB+BC+CA}{3} cm=_____ cm

Least Count of spherometer

Screw pitch (p) = _____ mm Total number of circular scale divisions, N = _____ Least count, (L.C.) = \frac{Screw \hspace{0.2cm}pitch}{Total \hspace{0.2cm} number \hspace{0.2cm} of \hspace{0.2cm} circular \hspace{0.2cm} scale \hspace{0.2cm} divisions} Least count, (L.C.) =____ mm

Table for determination of h

Calculations

R=\frac{l^{2}}{6h}+\frac{h}{2} R = ____ mm = ______ cm So, the radius of curvature of the given convex surface is _____ cm

Precautions and Discussions

• The screw should be moved in the same direction to avoid back-lash error of the screw.
• Excess rotation should be checked and avoided.
• The screw should rotate without any friction.

Viva questions on Spherometer experiment for class 11 and engineering physics practical

• What is the main principle behind the working of a spherometer? Answer: The spherometer works on the principle of micrometer screw.
• Why this instrument is called spherometer? Answer: It is called spherometer because it measures the radius of curvature of a spherical surface.
• Write down the formula for determination of radius of curvature of a spherical surface using spherometer? Answer: The radius of curvature of a spherical surface is given by R=\frac{l^{2}}{6h}+\frac{h}{2} Where l is the distance between any two legs of the spherometer and h is the perpendicular distance between the legs and screw when it is above the spherical surface
• What is the value of radius of curvature of a plane surface? Answer: The radius of curvature of a plane surface is infinite.
• What is the pitch of a spherometer? Answer: The pitch is defined as the linear distance travelled by the circular disc in one complete rotation.
• Write down the lens makers formula. Answer: The lens makers formula is given by \frac{1}{f}=[\frac{\mu_{2}}{\mu_{1}}-1][\frac{1}{R_{1}}-\frac{1}{R_{2}}]
• Can you measure the focal length of a lens by using spherometer. Answer: Yes, by measuring the radius of curvatures and putting these values in lens makers formula.
• Why good spherometers are made of gun metal? Answer: To minimize the wear and tear. Note: Gun metal is an alloy of Copper, tin and Zinc.

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• To Determine Radius of Curvature of a Given Spherical Surface by a Spherometer

We can define a spherometer as a measuring device which has a metallic triangular frame supported on three legs. The tips of these three legs form a triangle that is equilateral and which lie on the radius. In this article we will discover more things about the radius of curvature. There is a leg which is the central leg which can be moved in a direction which is perpendicular. In the below article there is the experiment on how to determine the radius of curvature of a given spherical surface by a spherometer.

To Determine Radius of Curvature of Spherical Surface

Aim of the Experiment: 

To determine radius of curvature of a given spherical surface by a spherometer.

Apparatus:  

a Spherometer for experiment, a convex surface (it may be an unpolished mirror), a big size plane glass slab or mirror which is plain.

Theory of Experiment:

The figure which is shown below is a schematic diagram of a single disk spherometer. It generally consists of a central legs which can be raised or lowered through a threaded hole V that is at the centre of the frame denoted by F. The triangular metallic frame F is supported on three legs of equal length A, B and C.  A vertical scale that is denoted by letter P marked in millimetres or half-millimetres, is known as the main scale or pitch scale. It is also fixed parallel to the central screw, which is at one end of the frame F. This scale is kept very close to the disc rim denoted by letter D but it does not touch the disc D. This scale generally reads the vertical distance when the central leg moves through the hole V. 

[Image will be Uploaded Soon]

Spherometer Experiment Procedure

Raise the central screw of the spherometer and then press the spherometer gently on the practical note-book to get pricks of the three legs. Then we need to mark these pricks as A, B and C.

Then measure the distance between the pricks and the points by joining the points to form a triangle ABC.

We need to note these distances which are: AB, BC, AC on a notebook and take their mean.

Then we need to find the value of one vertical pitch scale division.

Then determine the pitch and the least count of the spherometer and record it stepwise.

Raise the screw upwards sufficiently.

Place the spherometer on the convex surface so that its three legs rest on it.

Then we need to gently turn the screw downwards till the screw tip just touches the convex surface.

Now note the reading of the circular disc scale which is in line with the vertical scale pitch.

 Remove the spherometer from over the convex surface and place IT over a large size glass plane slab.

Then turn the screw downwards direction and count the number of complete rotations(n1) made by the disc. One rotation becomes complete when the reference reading crosses past the pitch scale.

We need to continue till the tip of the screw just touches the plane surface of the glass slab.

 Note the reading of the circular scale which is finally in line with the vertical pitch scale. Let it be denoted by letter b.

 Now find the number of circular disc scale divisions in the last rotation which is incomplete.

 Record the observation in tabular form.

The Calculations Part:

1.  We need to find the value of h in each observation and record it in the column.

2. Then find the mean of the value of h that is recorded in the column.

The Result: 

The radius of curvature of the given convex surface is cm.

The Precautions: 

The screw should move freely without friction .

The screw which we are talking about should be moved in the same direction to avoid the back-lash error of the screw.

Excess rotation that should be avoided.

The Sources of Error 

The screw may have friction.

The spherometer generally may have a back-lash error.

The circular disc scale divisions may not be of equal size.

What is Spherometer

A spherometer is said to be an instrument for the precise measurement of the radius of curvature of a sphere or that of a curved surface. originally these instruments were primarily used by opticians to measure the curvature of the surface of a lens..

FAQs on To Determine Radius of Curvature of a Given Spherical Surface by a Spherometer

Q1. Explain What is the Principle of the Spherometer?

Ans: The term spherometer works on the principle of the micrometer screw. It is generally used to measure either very small thickness of flat materials which is like glass or the radius of curvature of a spherical surface.

Q2. Explain Where the Spherometer is Used?

Ans: A spherometer is said to be an instrument for the precise measurement of the radius of curvature of a sphere or that of a curved surface. Originally we can notice that these instruments were primarily used by opticians to measure the curvature of the surface of a lens.

Q3. What is the Least Count of a Screw Gauge?

Ans: The least count of screw gauge is 0.01mm which is the minimum value up to which a screw gauge can measure. The least count is said to be defined as the ratio of pitch of the screw to the number of divisions on the circular scale.

Spherometer – Measure the radius of curvature of a spherical surface | Labkafe

Aim:  

To determine the radius of curvature of a given spherical surface by a Spherometer.  

Apparatus:  

• Spherometer
• Half Meter Scale
• Convex Lens

Theory:  

A spherometer is a measuring instrument used to measure the radius of curvature of a spherical surface and a very small thickness. 

Figure 3.1 is a schematic diagram of a single disk spherometer. It consists of a central leg OS, which can be raised or lowered through a threaded hole V (nut) at the centre of the frame F. The metallic triangular frame F supported on three legs of equal length A, B and C. The lower tips of the legs form three corners of an equilateral triangle ABC and lie on the periphery of a base circle of known radius, r. The lower tip of the central screw, when lowered to the plane (formed by the tips of legs A, B and C) touches the centre of triangle ABC. A circular scale (disc) D is attached to the screw.  The circular scale may have 50 or 100 divisions engraved on it. A vertical scale P marked in millimetres or half-millimetres, called main scale or pitch scale P is also fixed parallel to the central screw, at one end of the frame F. This scale is kept very close to the rim of disc D but it does not touch the disc D. This scale reads the vertical distance when the central leg moves through the hole V.   

Fig 3.1       

Principle:  

Pitch of a Spherometer  

            The vertical distance moved by the screw S in one complete rotation of the circular Scale/Disc D is called the pitch (p) of the spherometer. To find the pitch, give full rotation to the screw (say 4 times) and note the distance (d) advanced over the pitch scale. 

If the distance d is 4 mm The pitch can be represented as, 

Least Count of the Screw Gauge  

The Least count (LC) is the distance moved by the spherometer screw, when the screw is turned through 1 division on the circular. We are using a spherometer which has 100 divisions (N) on the disc. The least count can be calculated using the formula, 

The formula for the radius of curvature of a spherical surface  

Approach 1:  

From the figure 3.3, O is the centre of the circle. OE = OA = R, radius of the circle. F is the tip of the screw at the same plane with A, B and C. EF = h, AF = a and ∠AFO =   

Therefore, geometrically we can write, 

OA2 = OF2 + FA2 

or, R2    = (R-h)2 + a2 

= R2 -2.R.h + h2 + a2 

∴  R = (h2 + a2 )/2h  

Now, let  l  be the distance between any two legs of the spherometer as shown in figure 3.6, then from geometry we have, a = . Thus the radius of curvature of the spherical surface can be given by, 

               ∴ R = ( 3h2 + l2 )/6h         

Fig 3.3  

Approach 2:  

From the figure 3.4, the circle is passing through A and C.  O is the centre of the circle. OE =R, radius of the circle. F is the tip of the screw at the same plane with A, B and C. CF = h, AF = a ∠EAC = 900. 

∴ CE2 = AE2 + AC2 

or, (2R2) = (AF2 + FE2) + (CF2 + AF2) 

                  = a2 + (2R -h)2 + h2 + a2 

∴ R=  a2/2h+ h/2 

Now, let  l  be the distance between any two legs of the spherometer or the side of the equilateral triangle ABC (Fig. 3.4), then from geometry we have, a = l/√3. Thus the radius of curvature of the spherical surface can be given by, 

R =  a2/2h+ h/2 

or,  R = l2/6h+ h/2  

Diagram:   

Fig 3.4 

Fig 3.5  

Fig. 3.6  

Procedure:  

• Find the pitch (p) of the screw and count the total number of divisions (N) in the circular scale.
• Place the spherometer in the plane glass plate. Now rotate the head T anti-clockwise to raise the tip of the central screw S by a certain distance.
• Place the spherometer on the convex surface. Gently rotate T clockwise to bring down the tip of S until it just touches the spherical surface. Use a paper strip and try to pass between the tip of the screw and spherical surface to check if there is no gap between them.
• Record the initial circular scale reading (r1) in table 3.1. Circular scale reading means the divisions engraved on the disc which coincides with the linear scale.
• Place the spherometer on the glass slab without disturbing the initial circular scale reading (c.s.r). Then slowly rotate T clockwise to bring the tip down and touch the glass plate. During this rotation count the number of full rotation (n) of the circular scale. Take the final c.s.r. (r2) when the tip touches the glass plate.
• Repeat step 2 and 5 at least thrice by placing the spherometer at different places.
• Now, place the spherometer on a piece of paper and press it lightly so that an imprint of the three legs is made on the paper. You can do it on your laboratory notebook on the left side white page.
• Measure each side of the triangle AB, BC, and CA formed by the points  (A, B, C).
• Take mean of them. Thus we get l.

Observations:  

Least count of spherometer :  

Total number of divisions is the in circular scale, N = _______ 

One linear scale division, L.S.D.  = ____ mm 

Distance moved by the screw for 4 rotations, d = ________ mm 

Pitch of the screw, p = 4/d = ____mm 

Therefore, Least Count, L.C. = p/N= ______________mm 

Distance between two legs of spherometer:  

                AB = _______ cm, BC = _______cm, CA = _________cm 

∴ l = (AB + BC+ CA)/3 = _______________________cm 

Table 3.1 Table for height (h)  

Mean value of sagitta, h = _________________ mm = ________________cm 

Calculation:  

Radius of curvature of the given convex surface, R = (3h2 + l2 )/6h =…………………………..cm  

or, Radius of curvature of the given convex surface ,  R = l2/6h+ h/2 =……………………………   cm  

Precautions:  

• The screw should move freely without friction.
• The screw should be rotated in one direction to get any reading. Otherwise back-lash error will be introduced.
• The circular should not be rotated any more, even slightly, when it touches a surface.
• The linear scale is not used to take readings and h is calculated by taking the difference of two circular scale readings. Hence we do not need to find the zero error of the instrument.

Reference:  

• http://www.ncert.nic.in/

Your may checkout our blog on   SCREW GAUGE & LEAST COUNT    

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Spherometer: Determining Radius of Curvature of Spherical surface

What is a spherometer? How do you use it to determine the radius of curvature of a given spherical surface?

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Target Exam ---

To determine the radius of curvature of a given spherical surface by a spherometer.

Apparatus Spherometer, convex surface (it may be an unpolished convex mirror), a big size plane glass slab, or plane mirror.

Theory It works on the principle of micrometer screw. It is used to measure either very small thickness or the radius of curvature of a spherical surface which is why it is called a spherometer.

• Raise the central screw of the spherometer and press the spherometer gently on the practical notebook so as to get pricks off the three legs. Mark these pricks as A, B, and C.
• Measure the distance between the pricks (points) by joining the points to form a triangle ABC.
• Note these distances (AB, BC, AC) in the notebook and take their mean.
• Find the value of one vertical {pitch) scale division.
• Determine the pitch and the least count of the spherometer [Art. 2.13(c)] and record it step-wise.
• Raise the screw sufficiently upwards.
• Place the spherometer on the convex surface so that its three legs rest on it.
• Gently, turn the screw downwards till the screw tip just touches the convex surface. (The tip of the screw will just touch its image on the convex glass surface).
• Note the reading of the circular (disc) scale which is in line with the vertical (pitch) scale. Let it be a (It will act as a reference).
• Remove the spherometer from over the convex surface and place it over a large size plane glass slab.
• Turn the screw downwards and count the number of complete rotations (n 1 ) made by the disc (one rotation becomes complete when the reference reading crosses past the pitch scale).
• Continue till the tip of the screw just touches the plane surface of the glass slab.
• Note the reading of the circular scale which is finally in line with the vertical (pitch) scale. Let it be b.
• Find the number of circular (disc) scale divisions in the last incomplete rotation.
• Repeat steps 6 to 14, three times. Record the observation in tabular form.

Result The radius of curvature of the given convex surface is cm.

Precautions

• The screw should move freely without friction.
• The screw should be moved in the same direction to avoid the back-lash error of the screw.
• Excess rotation should be avoided.

Sources of error

• The screw may have friction.
• The spherometer may have a back-lash error.
• Circular (disc) scale divisions may not be of equal size.

Question.1. Describe the principle of a spherometer. Answer. It works on the principle of a micrometer screw.

Question.2. Why is a spherometer so called? Answer. It measures the radius of curvature of spherical surfaces, hence it is called a spherometer.

Question.4. What are the values of P and R? for a plane surface? Answer. For a plane surface, P = 0 and R = infinite.

Question.5. What is meant by the pitch of the spherometer? Answer. The pitch is the distance between two consecutive threads of the screw taken parallel to the axis of rotation or the distance moved by the screw in one complete rotation of the circular scale.

Question.6. How can the accuracy of a spherometer be increased? Answer. The smaller is the least count, the more is the accuracy of an instrument and vice versa. The accuracy of the spherometer can be increased by decreasing the pitch or by increasing the number of divisions of the circular scale.

Question.7. The least count of screw gauge and spherometer is the same. Which will you prefer to measure the radius of curvature of the lens or mirror? Answer. The spherometer.

Question.9. Can you measure the focal length of a lens? Answer. Yes, by measuring R 1 and R 2 by spherometer n 1 = 1 and n 2 is known refractive index of the material of the lens.

Question.10. Why is the good spherometer made of gunmetal? Answer. To minimize wear and tear.

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• class 11 to determine radius of curvature of a given spherical surface by a spherometer viva questions

To Determine Radius of Curvature of a Given Spherical Surface by a Spherometer - Physics Practical Class 11 Viva Questions with Answers

• What is a spherometer?

Answer. A spherometer is an instrument used to measure the radius of curvature of a curved surface or a sphere accurately.

• Spherometer works on what principle?

Answer. The spherometer works on the principle of the micrometer screw.

• Mention the least count of the spherometer.

Answer. The least count of the spherometer is 0.01mm.

• Define the pitch of the spherometer.

Answer. pitch is described as the distance advanced by the central screw in one complete rotation of the circular disc scale.

• What is the formula to calculate the least count of a spherometer?

Answer. The least count is given by the formula:

Least count = Pitch of the spherometer screw / Number of divisions on the circular scale

• What is the value of the pitch of the screw?

Answer . The Pitch of the screw is 1 mm.

• What is the formula to calculate the radius of curvature using a spherometer?

Answer. It is given by the formula:

\(\begin{array}{l}R=\frac{l^{2}}{6h}+\frac{h}{2}\end{array} \)

• Choose YES or NO: Can the central leg of the spherometer move in downward and upward directions?

Answer. YES. The central leg can be moved both upwards and downwards.

• What would be the distance moved by the screw in 10 complete rotations?

Answer . Distance moved by the screw in 10 complete rotations will be 10 mm

• What will be the number of divisions on the circular scale?

Answer. The number of divisions on the circular scale will be 100.

• Who invented the spherometer?

Answer. The spherometer was invented in 1810 by the French optician Robert-Aglae Cauchoix.

• For what purpose do astronomers use the spherometer?

Answer. Astronomers used a spherometer for grinding lenses and curved mirrors.

• Spherometer consists of how many outer legs?

Answer. The spherometer consists of three outer legs.

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