w1l - Douglass Houghton Workshop Section 1 Wed Worksheet...

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Douglass Houghton Workshop, Section 1, Wed 11/2/11 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. When a line makes an angle θ with the x -axis, it has slope tan θ . So if we call the angle between the normal line and the horizontal θ , then tan θ = b/ 2. x y 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 ) = 2tan( x ) 1 tan 2 ( x ) . (c) Write an equation for the reflected ray. (d) Where does the reflected ray intersect the x -axis? What is surprising about this answer? (e) Graph several rays, with their reflections. (f) What’s cool about this type of mirror?
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