hw7 - Phys 3327 Fall 2010 HW 7 Due Wednesday in lecture...

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Unformatted text preview: Phys 3327 Fall 2010 HW 7 Due Wednesday 10/27/10 in lecture Homework 7 Reﬂection and Refraction Ex. 3.1: Frustrated total internal reﬂection a) A light ray undergoes total internal reﬂection in a prism at an angle of incidence of π/4, see the left panel of the ﬁgure below. What is the minimal value of the index of refraction n of the material the prism is made of for this to happen? b) A second prism is held at a distance t from the prism of part (a), see the right panel of the ﬁgure above. The space between the prisms is ﬁlled with air. (Air has unit index of refraction.) What are the amplitudes of the reﬂected and transmitted waves in this case? Take the light to be polarized perpendicular to the plane of incidence. c) What are the reﬂection and transmission coeﬃcients R⊥ and T⊥ in this case? Explain the behavior of your answers in the limits t → 0 and t → ∞. Ex. 7.2: Secondary Rainbow Under suitable atmospheric conditions you can see two rainbows in the sky. The secondary rainbow is from light that reﬂects twice inside a single drop of rain. At what angle (compared to the direction of the sun) does the secondary rainbow appear? In what order do the colors appear in the secondary rainbow? Please explain your answers! (The index of refraction for water is nwater ≈ 1.333. It has a weak frequency dependence, dnwater /dω > 0.) Ex. 7.3: Brewster angle twice Heald & Marion, Ex 6-9. Suggested Heald & Marion problems for further study: 6-2 (Matching Impedances), 6-6 (Optical Length), 6-8 (Fresnel Formulas for magnetic media), 6-10 (Brewster angle and total internal reﬂection), 6-12 (Poynting vector for conditions of total internal reﬂection), 6-13 (Reﬂection oﬀ a conductor) 1 ...
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