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Unformatted text preview: honea (cth632) H9Refraction avram (1956) 1 This printout should have 25 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points A shallow pool of a liquid 7 . 4 m deep is not the depth one expects when viewed from over head. The index of refraction of the liquid is 1 . 35. How deep does it appear to be? Correct answer: 548 . 148 cm. Explanation: Basic Concepts n 1 s 1 + n 2 s 2 = n 2 n 1 R Solution: Consider a point on the bottom of the pool as our object. In the refraction surface formula n 1 s 1 + n 2 s 2 = n 2 n 1 R . Because the water surface of a pool is a plane, R = , thus n 2 n 1 R = 0. The object s 1 is under the water, n 1 = 1 . 35 is the index of refraction of water, and n 2 = 1 is the index of refraction of air. Hence, s 2 = s 1 n 2 n 1 = (7 . 4 m)(1) (1 . 35) = 5 . 48148 m . The image is virtual and on the same side of the interface as the object at a distance d apparent =  5 . 48148 m  = 548 . 148 cm. Note: One may also determine the apparent depth in an alternative approach. First sketch a ray diagram for a finite incident angle where the refacted ray hits the bottom of the pool at P. Draw a vertical line OP, where O is at the surface of the water, OP is the real depth. The apparent depth is defined by the depth OP, where P is the intersection between OP and the extrapolated line of the incident ray. We leave it an exercise for the reader to show that OP /OP = n 1 /n 2 . 002 10.0 points Batman and Robin are attempting to escape that dastardly villain, the Joker, by hiding in a large pool of water (refractive index n water = 1 . 333). The Joker stands gloating at the edge of the pool. (His makeup is water soluble.) He holds a powerful laser weapon y 1 = 1 . 33 m above the surface of the water and fires at an angle of 1 = 29 . 9 to the hor izontal. He hits the Boy Wonder squarely on the letter R, which is located y 2 = 3 . 92 m below the surface of the water. x y y 1 1 2 R J Batplastic surface Mirrored Surface water B How far (horizontal distance) is Robin from the edge of the pool? (Fear not, Batfans. The R is made of laserreflective material.) Correct answer: 5 . 66886 m. Explanation: Basic Concepts: Snells law, Total inter nal reflection. Solution: Let x 1 be the horizontal distance from the laser to where the laser beam strikes the water and x 2 the horizontal distance from that point to Robin (see the following figure). 1 x y 1 x y 2 2 air water J R 90 1 1 2 honea (cth632) H9Refraction avram (1956) 2 Then we have x 1 = y 1 tan 1 = (1 . 33 m) tan(29 . 9 ) = 2 . 31294 m ....
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 Spring '10
 Avram
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