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# Test IV - Version 145/ACBAB midterm 04 Turner(60230 This...

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Version 145/ACBAB – midterm 04 – Turner – (60230) 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A jewel thief decides to hide a stolen diamond by placing it at the bottom of a crystal-clear fountain. He places a circular piece of wood on the surface of the water and anchors it directly above the diamond at the bottom of the fountain. d 0 . 7 m If the fountain is 0.700 m deep, find the minimum diameter, d of the piece of wood that would prevent the diamond from being seen from outside the water. 1. 3.40363 2. 1.58836 3. 1.83796 4. 2.7229 5. 3.85744 6. 4.08435 7. 2.26908 8. 3.17672 9. 2.49599 10. 1.9741 Correct answer: 1 . 58836 m. Explanation: Basic Concept: sin θ c = n r n i Given: n i = 1 . 333 n r = 1 . 00 Δ y = 0 . 700 m Solution: θ c = sin 1 parenleftbigg n r n i parenrightbigg = sin 1 parenleftbigg 1 1 . 333 parenrightbigg = 48 . 6066 tan θ c = d 2 Δ y = d y d = 2Δ y (tan θ c ) = 2(0 . 7 m)(tan 48 . 6066 ) = 1 . 58836 m 002 10.0 points A thin lens has a crescent shape, which is defined by two spherical surfaces A and B . The radius of the surface A is | R A | = 3 a , and of surface B is | R B | = a and the index of refraction of the lens is 2.0. A B a 3 a O C A C B What is the focal length using the small angle approximation? 1. f = - 3 4 a 2. f = - 1 3 a 3. f = 3 2 a correct 4. f = - 1 4 a 5. f = 3 a 6. f = 4 a 7. f = - a

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Version 145/ACBAB – midterm 04 – Turner – (60230) 2 8. f = - 1 2 a 9. f = 5 2 a 10. f = 2 a Explanation: R 1 is the x -coordinate of the center of the spherical surface A ; i.e. , R 1 = -| R A | = - 3 a . Similarly, R 2 = - a . The lens maker’s formula gives 1 f = ( n - 1) parenleftbigg 1 R 1 - 1 R 2 parenrightbigg = (2 - 1) parenleftbigg 1 - 3 a - 1 - a parenrightbigg = 2 3 a . Hence, f = 3 2 a . 003 10.0 points Which travels most slowly in glass? 1. Red light 2. Green light 3. Orange light 4. Brown light 5. Yellow light 6. Violet light correct 7. Blue light Explanation: n = c v Since violet light is refracted more than the light of other frequencies its index of re- fraction is the highest, making its speed the smallest. In other words, violet light travels slowest in glass. 004 10.0 points A coin 1 . 05 cm in diameter is embedded in a solid glass ball of radius 38 . 3 cm(see the figure). n d p 1 n 2 > n 2 n 1 The index of refraction of the ball is 1 . 64, and the coin is p = 19 . 8 cm from the surface. Find the distance the image’s position is from the surface of the glass ball. 1. 12.884 2. 13.8881 3. 13.1187 4. 16.6466 5. 12.5449 6. 14.7349 7. 15.1245 8. 11.3205 9. 14.4782 10. 12.1357 Correct answer: 15 . 1245 cm. Explanation: Because n 1 > n 2 , where n 1 = 1 . 64 is the index of refraction of the ball and n 2 = 1 . 00 is the index of refraction of the air, the rays are refracted away from the normal at the surface and diverge outward. Hence, the image is formed in the glass and is virtual. Applying the equation n 1 p + n 2 q = n 2 - n 1 R , with d = | q | and R = - 38 . 3 cm , we get q = n 2 bracketleftbigg n 2 - n 1 R - n 1 p bracketrightbigg 1 = (1) bracketleftbigg (1) - (1 . 64) ( - 38 . 3 cm) - (1 . 64) (19 . 8 cm) bracketrightbigg 1
Version 145/ACBAB – midterm 04 – Turner – (60230) 3 = - 15 . 1245 cm d = | q | = 15 . 1245 cm .

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Test IV - Version 145/ACBAB midterm 04 Turner(60230 This...

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