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 Bouncy Bouncy Part 1 (Posted on 2006-02-08)
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 | 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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