Part 1: Laser
A laser is fired at a flat mirror.
The laser beam starts at the point (0,5) following the equation y = 5  x/3 heading down to the right.
The mirror follows the equation y=x/2.
Find the equation for the path the beam takes after it hits the mirror.
The point of reflection is the intersection of lines
y = 5  x/3 and y = x/2
or
(6,3)
The incident vector (towards source) is
I = 3i + j
The normal vector is
N = i + 2j
The reflection vector is
R = i + mj
Therefore,
dot(I,N) dot(R,N)
 = 
I R
or
dot(3i + j,i + 2j) dot(i + mj,i + 2j)
 = 
sqrt(3^2 + 1^1) sqrt(1^2 + m^2)
or
5 1 + 2m
 = 
sqrt(10) sqrt(1 + m^2)
or
(3m + 1)(m  3) = 0
m = 1/3 is the incident vector and
m = 3 is the reflection vector
Therefore, the line y = mx + k through the point (6,3) is
y = 3(x  5)

Posted by Bractals
on 20060208 12:27:29 