In Bouncy Bouncy Part 1 you were to find the equation for the path of a laser reflected off of a flat mirror. The slopes of each were specified.
The challenge now is to find a general formula for the new slope of any laser with slope a reflecting off a mirror of slope b.
Use of trigonometry is acceptable, but not required.
Let a' be the slope of the reflected laser.
Clearly, arctan(a) + arctan(a') = 2 arctan(b).
Applying the trig. identity for the tangent of
the sum of two angles to this gives
a + a' 2b
 = 
1  aa' 1  b^2
Solving for a' gives
b(ab + 2)  a
a' = 
b(2a  b) + 1

Posted by Bractals
on 20060323 21:40:57 