**Pfund’s Method for Measuring the Index of Refraction of Glass**A. H. Pfund's method for measuring the index of refraction of glass is illustrated in the figure. One face of a glass slab of thickness \( t \) is painted white, and a small hole scraped clear at point \( P \) acts as a source of diverging rays when the slab is illuminated from below. Ray \( PBB' \) strikes the clear surface at the critical angle and is totally reflected, as are rays such as \( PCC' \). Rays such as \( PAA' \) emerge from the clear surface. On the painted surface, a dark circle of diameter \( d \) appears, surrounded by an illuminated region, or halo.### Diagram Explanation:- The diagram shows rays originating from point \( P \) at the painted surface of the slab, traveling upwards.- Rays hitting the clear surface at less than the critical angle emerge, while rays hitting at exactly the critical angle are totally internally reflected.- The reflection creates a dark circle of diameter \( d \), seen on the painted surface.### Questions:(a) **Derive an Equation for \( n \):** Derive an equation for the index of refraction \( n \) in terms of the measured quantities \( d \) and \( t \). \[ n = \](b) **Calculate Diameter:** What is the diameter of the dark circle if \( n = 1.45 \) for a slab 0.520 cm thick? \[ \text{Diameter} = \_\_ \text{cm} \](c) **Effect of Dispersion:** If white light is used, dispersion causes the critical angle to depend on color. Is the inner edge of the white halo tinged with red light or with violet light? - [ ] violet - [ ] red--- This explanation covers the theoretical setup and provides questions to guide the measurement and analysis using Pfund's method.

Answered: Image /qna-images/answer/dcff3fc8-41b9-4274-be5c-bb13eac84f55.jpg

A. H. Pfund's method for measuring the index of refraction of glass is illustrated in the figure below. One face of a slab of thickness t is painted white, and a small hole scraped clear at point P serves as a source of diverging rays when the slab is illuminated from below. Ray PBB' strikes the clear surface at the critical angle and is totally reflected, as are rays such as PCC. Rays such as PAA' emerge from the clear surface. On the painted surface, there appears a dark circle of diameter d surrounded by an illuminated region, or halo. C' B' n= CBA Clear surface Painted surface (a) Derive an equation for n in terms of the measured quantities d and t. (b) What is the diameter of the dark circle if n = 1.45 for a slab 0.520 cm thick? cm 4 (c) If white light is used, dispersion caused the critical angle to depend on color. Is the inner edge of the white halo tinged with red light or with violet light? O violet O red

A. H. Pfund's method for measuring the index of refraction of glass is illustrated in the figure below. One face of a slab of thickness t is painted white, and a small hole scraped clear at point P serves as a source of diverging rays when the slab is illuminated from below. Ray PBB' strikes the clear surface at the critical angle and is totally reflected, as are rays such as PCC. Rays such as PAA' emerge from the clear surface. On the painted surface, there appears a dark circle of diameter d surrounded by an illuminated region, or halo. C' B' n= CBA Clear surface Painted surface (a) Derive an equation for n in terms of the measured quantities d and t. (b) What is the diameter of the dark circle if n = 1.45 for a slab 0.520 cm thick? cm 4 (c) If white light is used, dispersion caused the critical angle to depend on color. Is the inner edge of the white halo tinged with red light or with violet light? O violet O red

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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