Assignment 1 - (b ψ x t = A sin a z 2-b t 2(c ψ x t = A...

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PHYS 434 Optics Problem set #1 1. What length mirror must you purchase to see your full height when it is mounted in a vertical position? Do not assume you have eyes on the top of your head. 2. A parking lot is illuminated at night by identical lamps at the top of two poles 9m high and 12m apart. Assuming the lamps radiate equally in all directions, compare the irradiance (intensity) at ground level for the points directly under one lamp and midway between them. 3. Prove that the reflected ray from a plane mirror turns through an angle 2 θ when the mirror turn through θ . 4. Determine which of the following describe traveling waves: (a) ψ ( y, t ) = e ( - a 2 y 2 + b 2 t 2
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Unformatted text preview: ) (b) ψ ( x, t ) = A sin( a z 2-b t 2 ) (c) ψ ( x, t ) = A sin ( 2 π ± x a + t b ) 2 ² (d) ψ ( x, t ) = A cos 2 (2 π ( t-x )) . Where appropriate draw the profile and find the speed and direction of motion. 5. A small goldfish is viewed through a spherical glass fishbowl 30 cm in diameter. Deter-mine the apparent position and magnification of the fish’s eye when its actual position is (a) at the center of the bowl and (b) halfway between the center and the glass, along the line of sight, nearest to viewer. Assume that the glass is thin enough so that its effect on the refraction may be neglected....
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