experiment to find angle of prism using spectrometer

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Prism Spectrometer

The prism spectrometer

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The refractive index is one of the basic descriptors of materials that we use for their optical properties. It governs the design of lenses and other optical components, such as photonic devices in fibre optic communication systems. By studying a prism made from the material of interest, you can accurately measure the refractive index.  

Rays passing through the prism deviate because of refraction. Simply ray (geometrical) optics and the use of Snell’s law shows that the index is directly related to the minimum angular deviation of a ray that passes through the prism at different angles of incidence.  

In this experiment, you will use a spectrometer to measure the minimum deviation angle of light passing through a prism and use that to calculate the refractive index. A cadmium lamp provides a few discrete wavelengths; for each wavelength, the minimum deviation angle will be different. This is because the prism refractive index varies with wavelength (the property known as “dispersion”), so this property can be measured as well.  

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Determination of the angle of prism

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In the measurement of the angle of a prism using a spectrometer, the readings of first reflected image are Vernier I : 320 o 40 ′ ; Vernier I I : 140 o 30 ′ and those of the second reflected image are Vernier I : 80 o 38 ′ Vernier I I : 260 o 24 ′ . Then the angle of the prism is 59 o 58 ′ 59 o 56 ′ 60 o 2 ′ 60 o 4 ′ 60 o 0 ′

For vernier one, the difference in the reading = 320 ∘ 40 ′ − 80 ∘ 38 ′ = 240 ∘ 02 ′ for vernier two, the difference in the reading = 260 ∘ 24 ′ − 140 ∘ 30 ′ = 119 ∘ 24 ′ so the difference in the reading 2 φ = 240 ∘ 02 ′ − 119 ∘ 24 ′ = 120 ∘ 08 ′ ∴ φ = 120 ∘ 08 ′ 2 = 60 ∘ 04 ′.

A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading : 58.5 degree Vernier scale reading : 09 divisions Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of prism from the above data is

A vernier callipers has its main scale graduated in mm and 10 divisions on its vernier scale are equal in length to 9 mm. When the two jaws are in contact, the zero of vernier scale is ahead of zero of main scale and 3rd division of vernier scale coincides with a main scale division. Find : (i) the least count and (ii) the zero error of the vernier callipers.

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• Published: 11 September 2024

Controllable p- and n-type behaviours in emissive perovskite semiconductors

• Wentao Xiong   ORCID: orcid.org/0009-0003-4139-9011 1 ,
• Weidong Tang 1 ,
• Gan Zhang 1 ,
• Yichen Yang 1 ,
• Yangning Fan 1 ,
• Ke Zhou 1 ,
• Chen Zou 1 , 2 ,
• Baodan Zhao   ORCID: orcid.org/0000-0002-4006-7061 1 , 2 &
• Dawei Di   ORCID: orcid.org/0000-0003-0703-2809 1 , 2  

Nature volume  633 ,  pages 344–350 ( 2024 ) Cite this article

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• Chemical physics
• Electronic devices
• Electronic materials
• Electronic properties and materials
• Lasers, LEDs and light sources

Reliable control of the conductivity and its polarity in semiconductors is at the heart of modern electronics 1 , 2 , 3 , 4 , 5 , 6 , 7 , and has led to key inventions including diodes, transistors, solar cells, photodetectors, light-emitting diodes and semiconductor lasers. For archetypal semiconductors such as Si and GaN, positive (p)- and negative (n)-type conductivities are achieved through the doping of electron-accepting and electron-donating elements into the crystal lattices, respectively 1 , 2 , 3 , 4 , 5 , 6 . For halide perovskites, which are an emerging class of semiconductors, mechanisms for reliably controlling charge conduction behaviours while maintaining high optoelectronic qualities are yet to be discovered. Here we report that the p- and n-type characteristics in a wide-bandgap perovskite semiconductor can be adjusted by incorporating a phosphonic acid molecular dopant with strong electron-withdrawing abilities. The resultant carrier concentrations were more than 10 13  cm −3 for the p- and n-type samples, with Hall coefficients ranging from −0.5 m 3  C −1 (n-type) to 0.6 m 3  C −1 (p-type). A shift of the Fermi level across the bandgap was observed. Importantly, the transition from n- to p-type conductivity was achieved while retaining high photoluminescence quantum yields of 70–85%. The controllable doping in the emissive perovskite semiconductor enabled the demonstration of ultrahigh brightness (more than 1.1 × 10 6  cd m −2 ) and exceptional external quantum efficiency (28.4%) in perovskite light-emitting diodes with a simple architecture.

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Data availability

The data supporting the findings of this study are available within the paper and its  Supplementary Information . The source data files are available at Figshare ( https://doi.org/10.6084/m9.figshare.26048218 ) 56 .

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Acknowledgements

This work was supported by the National Key Research and Development Program of China (grant no. 2022YFA1204800), the National Natural Science Foundation of China (grant nos. 62274144 and 62005243), the Zhejiang Provincial Government, the Natural Science Foundation of Zhejiang Province (grant no. LR21F050003) and the Fundamental Research Funds for the Central Universities. We acknowledge W. Guo and J. Zhang of Juanhu Lake Laboratory for the KPFM measurements, T. Sun and Z. Wang of Zhejiang University of Technology for the STEM measurements, and Y. Yang of the International Research Center for Functional Polymers at Zhejiang University for NMR and FTIR measurements. We thank the technicians at Shenzhen Huasuan Technology for their assistance with the theoretical calculations. We thank J. Sun from Shiyanjia Lab for the inductively coupled plasma optical emission spectroscopy (ICP-OES) measurements. We thank T. Liu of Guangxi University for assistance with device encapsulation.

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State Key Laboratory of Extreme Photonics and Instrumentation, College of Optical Science and Engineering, International Research Center for Advanced Photonics, Zhejiang University, Hangzhou, China

Wentao Xiong, Weidong Tang, Gan Zhang, Yichen Yang, Yangning Fan, Ke Zhou, Chen Zou, Baodan Zhao & Dawei Di

ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou, China

Chen Zou, Baodan Zhao & Dawei Di

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Contributions

D.D., B.Z. and W.X. conceived the study. W.X. planned the experiments under the guidance of D.D and B.Z. W.X. fabricated the efficient and bright HTL-free PeLEDs, characterized the devices and analysed the data. W.X. prepared the doped perovskite samples. W.X. and W.T. performed the UPS and XPS measurements. G.Z. performed the device simulations using COMSOL. W.X. and W.T. prepared the perovskite p–n junction diodes. C.Z., Y.Y. and Y.F. performed the transient photoluminescence measurements. W.X., W.T. and K.Z. performed the Hall effect measurements. W.X. prepared the initial draft of the manuscript, which was revised by D.D. and B.Z. All authors contributed to the work and commented on the paper. D.D. and B.Z. supervised the project.

Corresponding authors

Correspondence to Baodan Zhao or Dawei Di .

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Competing interests.

D.D., W.X. and B.Z. are inventors on CN patent application no. 202410202637.2. The other authors declare no competing interests.

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Extended data figures and tables

Extended data fig. 1 structural characterization of undoped and 4pacz-doped perovskite samples..

a , XRD patterns. b,c , The STEM images of undoped and 4PACz-doped perovskite samples, respectively. d,e , The SEM images of undoped and 4PACz-doped perovskite samples, respectively (scale bar: 500 nm). f,g , The AFM height images of undoped and 4PACz-doped perovskite samples, respectively (scale bar: 400 nm). R q denotes the root mean square (r.m.s.) of roughness.

Extended Data Fig. 2 Characterization of chemical interactions in solution and solid films.

a , 31 P NMR spectra of 4PACz, and 4PACz with PbBr 2 in deuterated DMSO. Compared with pure 4PACz compound, the 31 P NMR signals of 4PACz/PbBr 2 undergo an upfield shift, indicating the binding between the PA moiety on 4PACz and the Pb 2+ cations. b , 1 H NMR of 4PACz in deuterated-DMSO solution with FABr. * indicates protons on ammonium. The 1 H NMR results demonstrate the formation of hydrogen bonding between 4PACz and FA + , which could significantly affect the crystallization process of perovskite films during spin-coating. c , XPS spectra (O 1s ) of 4PACz and 4PACz-doped perovskites. Two peaks (P-OH groups at 533.6 eV, and P=O group at 532.3 eV) can be identified from the O 1s spectrum of 4PACz, while the O 1s spectrum of 4PACz-doped perovskites can be constructed by three peaks (P-OH groups at 532.6 eV, P=O group at 531.6 eV, and P-O-Pb group at 530.7 eV). The emergence of the new peak at around 530.7 eV indicates the presence of covalent bonding between Pb 2+ and the P-OH group on 4PACz through deprotonation process. d , XPS spectra (P 2p ) of 4PACz and 4PACz-doped perovskite. P 2p spectrum of 4PACz show the main peak at 134.6 eV, while shifting to 133.2 eV after doping into perovskites. The P 2p spectra of 4PACz (134.6 eV) and 4PACz-doped perovskite (133.2 eV) show similar spectral shapes, indicating that no bonding is formed between the perovskite and the P atom on 4PACz. e , XPS spectra (Pb 4f ) of undoped and 4PACz-doped perovskite samples. The Pb 4f peak of the perovskite films show a shift of ~0.2 eV to higher binding energies with the incorporation of 4PACz. This may be attributed to the formation of new Pb-O-P bonds in the solid films. The XPS results show that the electron densities on O and P atoms increase as the electron density around Pb 2+ decreases, highlighting the important role of the electron-withdrawing process during 4PACz doping. f , FTIR spectra of pristine 4PACz and 4PACz-doped perovskite. The stretching vibration peak of the P-O bond in 4PACz at 1058 cm −1 shifts to 1051 cm −1 with PbBr 2 , indicating the interactions between the PA group on 4PACz and Pb 2+ .

Extended Data Fig. 3 Additional device performance data of HTL-free PeLEDs.

a , Current density–voltage curves. b , Luminance-voltage curves. c , EQE-luminance curves. d , EL spectra.

Extended Data Fig. 4 Performance of undoped PeLEDs based on bare and 4PACz-coated ITO.

a , Current density–voltage curves. b , Luminance-voltage curves. c , EQE-luminance curves. g , η ECE -luminance curves.

Extended Data Fig. 5 Performance of doped PeLEDs based on bare and 4PACz-coated ITO.

a , Current density–voltage curves. b , Luminance-voltage curves. c , EQE-luminance curves.

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Xiong, W., Tang, W., Zhang, G. et al. Controllable p- and n-type behaviours in emissive perovskite semiconductors. Nature 633 , 344–350 (2024). https://doi.org/10.1038/s41586-024-07792-4

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Received : 12 December 2023

Accepted : 05 July 2024

Published : 11 September 2024

Issue Date : 12 September 2024

DOI : https://doi.org/10.1038/s41586-024-07792-4

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