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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 x-axis 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 x-axis? (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