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# Assign8 - PHY 54 Assignment 8 Summer 2011 Reading Light Key...

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Reading : Light Key concepts: Huygens’s principle; reflection; refraction; reflectivity; total reflection; Brewster angle; polarization by absorption, reflection and Rayleigh scattering. 1. Questions about reflected intensity. [Use the formulas on p. 7 of Light .] a. Show that at normal incidence the reflectivity is R = ( n 1 n 2 ) 2 ( n 1 + n 2 ) 2 , no matter which index is larger. b. Show that the sum of the Brewster angles for incidence from medium 1 and from medium 2 is 90°. c. Show that if there is a critical angle it is larger than the Brewster angle. d. Show that R > R except at normal incidence and when both are 1. 2. A beam of light in air has a square cross section of width d 1 . It is shown from the side, incident on a glass plate. a. The refracted beam is widened in the dimension shown, to d 2 . (The dimension normal to the page is unchanged.) Express d 2 / d 1 in terms of the angle of incidence θ 1 and the angle of refraction θ 2 . b. Suppose this beam consists of light with E in the plane of incidence, and let θ 1 be the Brewster angle so there is no reflected beam. Express d 2 / d 1 in terms of n , the refractive index of the glass. c. With no reflected beam, the power passing through a cross-section must be the same in both beams. What is the ratio of the intensities I 2 / I 1 ? 3. A rod made of transparent plastic is immersed in a liquid in a glass beaker, and is being viewed from the side as shown. a. Despite both the plastic and water being transparent, one can easily see the rod in the water. How? What light rays allow us to distinguish the plastic from the water? b. Suppose instead of water the liquid is an oil with the same index of refraction as that of the plastic. How would this affect our ability to see the plastic rod? Explain. θ 1 d 1 d 2 PHY 54 Assignment 8 Summer 2011

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4. Explain three things about sunset on a day with only scattered clouds. a. The sun is still visible for several minutes after it has “really” set. That is, without the atmosphere the sun would disappear earlier than it does with the atmosphere.
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Assign8 - PHY 54 Assignment 8 Summer 2011 Reading Light Key...

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