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Bouncy Bouncy Part 1 (Posted on 2006-02-08) Difficulty: 2 of 5
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.

See The Solution Submitted by Jer    
Rating: 4.0000 (2 votes)

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Solution Solution | Comment 4 of 10 |
 
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 2006-02-08 12:27:29
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