This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 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 xaxis, 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 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 ) . (c) Write an equation for the reflected ray. (d) Where does the reflected ray intersect the xaxis? What is surprising about this answer?...
View
Full
Document
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

Click to edit the document details