A laser beam of intensity I reflects from a flat, totally reflecting surface of area A whose normal makes an angle θ with the direction of the beam. Write an expression for the radiation pressure Pr[θ] exerted on the surface, in terms of the pressure Pr[p] that would be exerted if the beam were perpendicular to the surface.
Radiation Pressure equation for total reflection back along the original path.
Pr[p] = 2*I/c
The Attempt at a Solution
See attached picture.
Assuming F[θ] = F[p] = I*A / c
Use geometry to find F[θ]y
F[θ]y = Cos(θ) * F[θ]
Divide the equation by A to find pressure:
Pr[θ]y = Cos(θ) * Pr[θ]
Assuming Pr[θ] = Pr[p]
Pr[θ]y = Cos(θ) * Pr[p]
Since the beam is totally reflected, multiply by 2,
Pr[θ]y = 2 * Cos(θ) * Pr[p]
The correct answer is (Cos(θ))^2*Pr[p]
I'm really lost. I don't know how the cos function gets squared. Please help. Thanks in advance, MrMoose