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Unformatted text preview: Douglass Houghton Workshop, Section 2, Thu 11/3/11 Worksheet Labradoodle 1. Last time we thought about a parabolic mirror in the shape of the graph of y = ± √ 4 x . So far we’ve found: A light ray y = b hits the mirror at P = ( b 2 / 4 , b ). The slope of the tangent at that point is 2 /b . The normal line at the same point has slope b/ 2. A line that makes an angle θ with the xaxis has slope tan θ . So if we call the angle between the normal line and the horizontal θ , then tan θ = b/ 2. If a light ray bounces off a mirror, the angle between the incoming ray and the normal line is the same as the angle between the outgoing ray with the normal line. x y b P θ (a) To the ray, the mirror looks flat, just like the tangent line. Draw the reflected ray. What angle does it make with the xaxis? (b) What is the slope of the reflected ray? Put your answer in terms of b . Hint: tan(2 x ) = 2 tan( x ) 1 − tan 2 ( x ) ....
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This note was uploaded on 01/28/2012 for the course MATH 146 taught by Professor Conger during the Winter '08 term at University of Michigan.
 Winter '08
 Conger
 Slope

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