Old Exam 4 Sol

# Old Exam 4 Sol - Platt David – Oldquiz 4 – Due Dec 4...

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Unformatted text preview: Platt, David – Oldquiz 4 – Due: Dec 4 2005, 4:00 am – Inst: Ken Shih 1 This print-out should have 28 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 69 ◦ , as shown in the figure. A light ray strikes the horizontal mirror at an angle of 45 ◦ with respect to the mirror’s surface. 69 ◦ 45 ◦ φ Figure is not drawn to scale. Calculate the angle φ . Correct answer: 42 ◦ . 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(69 ◦ ) = 42 ◦ . As a matter of interest, in the upper-half of the figure the angles (clockwise) in the triangles from left to right are 45 ◦ , 45 ◦ , and 90 ◦ ; 90 ◦ , 21 ◦ , and 69 ◦ ; 111 ◦ , 24 ◦ , and 45 ◦ ; 135 ◦ , 24 ◦ , and 21 ◦ ; and in the lower-half of the figure the angles (counter-clockwise) in the triangles from left to right are 24 ◦ , 24 ◦ , and 132 ◦ ; 48 ◦ , 21 ◦ , and 111 ◦ ; 69 ◦ , 45 ◦ , and 66 ◦ ; 114 ◦ , 45 ◦ , and 21 ◦ . 002 (part 1 of 1) 10 points The reflecting surfaces of two intersecting flat mirrors are at an angle of 63 ◦ , 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. 63 ◦ φ Platt, David – Oldquiz 4 – Due: Dec 4 2005, 4:00 am – Inst: Ken Shih 2 Figure is not drawn to scale. Calculate the angle φ . Correct answer: 54 ◦ . 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(63 ◦ ) = 54 ◦ . As a matter of interest, in the upper-half of the figure the angles (clockwise) in the triangles from left to right are 46 ◦ , 46 ◦ , and 88 ◦ ; 92 ◦ , 27 ◦ , and 61 ◦ ; 119 ◦ , 17 ◦ , and 44 ◦ ; 136 ◦ , 17 ◦ , and 27 ◦ ; and in the lower-half of the figure the angles (counter-clockwise) in the triangles from left to right are 17 ◦ , 17 ◦ , and 146...
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## This note was uploaded on 07/26/2009 for the course PHY 303L taught by Professor Turner during the Fall '08 term at University of Texas.

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Old Exam 4 Sol - Platt David – Oldquiz 4 – Due Dec 4...

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