# oldq4 - Shie Gary – Oldquiz 4 – Due 1:00 pm – Inst...

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Unformatted text preview: Shie, Gary – Oldquiz 4 – Due: Nov 27 2004, 1:00 pm – Inst: Turner 1 This print-out should have 29 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points The reflecting surfaces of two intersecting flat mirrors are at an angle of 50 ◦ , as shown in the figure. A light ray strikes the horizon- tal mirror, reflects off the horizontal mirror, impinges on the raised mirror, reflects off the raised mirror, and proceeds in the right-hand direction. 50 ◦ φ Figure is not drawn to scale. Calculate the angle φ . Correct answer: 80 ◦ . Explanation: Basic Concept: θ incident = θ reflected Solution: θ 1 θ 2 φ θ Figure is to scale. The sum of the angles in a triangle is 180 ◦ . In the triangle on the left we have angles θ , 180 ◦- θ 1 2 , and 180 ◦- θ 2 2 , so 180 ◦ = θ + 180 ◦- θ 1 2 + 180 ◦- θ 2 2 , or θ 1 + θ 2 = 2 θ . (1) In the triangle on the right we have angles θ 1 , θ 2 , and φ. 180 ◦ = θ 1 + θ 2 + φ, so θ 1 + θ 2 = 180 ◦- φ. (2) Combining Eq. 1 and 2, we have φ = 180 ◦- 2 θ = 180 ◦- 2(50 ◦ ) = 80 ◦ . As a matter of interest, in the upper-half of the figure the angles (clockwise) in the triangles from left to right are 33 ◦ , 33 ◦ , and 114 ◦ ; 66 ◦ , 40 ◦ , and 74 ◦ ; 106 ◦ , 17 ◦ , and 57 ◦ ; 123 ◦ , 17 ◦ , and 40 ◦ ; and in the lower-half of the figure the angles (counter-clockwise) in the triangles from left to right are 17 ◦ , 17 ◦ , and 146 ◦ ; 34 ◦ , 40 ◦ , and 106 ◦ ; 74 ◦ , 33 ◦ , and 73 ◦ ; 107 ◦ , 33 ◦ , and 40 ◦ . 002 (part 1 of 1) 10 points Assume: Refraction index for diamond n diamond = 2 . 48 . The smallness of the critical angle θ c for di- amond means that light is easily “trapped” within a diamond and eventually emerges from the many cut faces. This makes a dia- mond more brilliant than stones with smaller n and larger θ c . Traveling inside a diamond, a light ray is incident on the interface between diamond and air. Shie, Gary – Oldquiz 4 – Due: Nov 27 2004, 1:00 pm – Inst: Turner 2 What is the critical angle for total internal reflection? Correct answer: 23 . 78 ◦ . Explanation: Basic Concept: Critical angle θ c for total internal reflection sin θ c = n 2 n 1 . Solution: For diamond, the critical angle sin θ c = 1 2 . 48 . θ c = 23 . 78 ◦ . 003 (part 1 of 1) 10 points 3 . 95 μ m θ Determine the maximum angle θ for which the light rays incident on the end of the light pipe shown in the figure above are subject to total internal reflection along the walls of the pipe. The pipe of diameter 3 . 95 μ m has an index of refraction of 1 . 38 and the outside medium is air....
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oldq4 - Shie Gary – Oldquiz 4 – Due 1:00 pm – Inst...

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