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Unformatted text preview: aldawsari (ma28683) – HW18 – Betancourt – (16856) 1 This printout should have 14 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 33.133.6 001 (part 1 of 3) 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 . 46 m above the surface of the water and fires at an angle of θ 1 = 26 . 9 ◦ to the hor izontal. He hits the Boy Wonder squarely on the letter “R”, which is located y 2 = 4 . 79 m below the surface of the water. θ 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: 7 . 18941 m. Explanation: Basic Concepts: Snell’s 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 θ 90θ ο 1 1 θ 2 Then we have x 1 = y 1 tan θ 1 = (1 . 46 m) tan(26 . 9 ◦ ) = 2 . 87782 m . From Snell’s law, n air sin(90 ◦ θ 1 ) = n water sin θ 2 . So sin θ 2 = sin(90 ◦ 26 . 9 ◦ ) (1 . 333) = 0 . 669015 θ 2 = arcsin(0 . 669015) = 41 . 9911 ◦ . Hence, x 2 = y 2 tan θ 2 = (4 . 79 m) tan41 . 9911 ◦ = 4 . 31159 m . Therefore, the distance of Robin from the edge of the pool is x 1 + x 2 = 2 . 87782 m + 4 . 31159 m = 7 . 18941 m . 002 (part 2 of 3) 10.0 points Batman attempts to hide out in a Batbox. The top is a mirrored surface, but the vertical sides are made of clear Batplastic (refractive index n p = 1 . 333). It is located x = 2 . 55 m horizontally from the edge of the pool. What is the minimum depth (measured to the top of the Batbox) that the Batbox can be below the surface of the water for the Caped Crusader to remain hidden from the Joker? Assume: The Joker gets down close to the water for the best view. Correct answer: 2 . 89308 m. Explanation: The mirrored surface will prevent Bat man’s being seem through the top of the box. We rely on total internal reflection at aldawsari (ma28683) – HW18 – Betancourt – (16856) 2 the Batplasticair interface to prevent his be ing seen through the side. Since n Batplastic = n water , there will be no reflection or refrac...
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 Spring '10
 Gavrine
 Snell's Law, Sin, Correct Answer, Total internal reflection, Betancourt

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