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 2006-03-23 21:40:57