Radiation Pressure — Question 2

Question 2

Two projection factors enter pressure on an oblique mirror

A broad vacuum beam of intensity I strikes a stationary perfect plane mirror of physical area A. Its incidence angle theta is measured from the normal. The illuminated mirror is entirely inside the beam.

1. Derive the intercepted power and normal force.

2. Find normal pressure at 60 degrees relative to normal incidence, and determine the tangential force.

Question 2 - Solution

Two projection factors enter pressure on an oblique mirror

(a) Method and calculation

$$P_{\mathrm{hit}}=IA\cos\theta,\quad\Delta p_n/U=2\cos\theta/c.$$$$\boxed{F_n=2IA\cos^2\theta/c}.$$

(b) Interpretation and further calculation

$$\boxed{p_n=2I\cos^2\theta/c,\quad p_n(60^\circ)/p_n(0)=1/4}.$$$$p_{t,\mathrm{in}}=p_{t,\mathrm{out}}\Rightarrow\boxed{F_t=0}.$$

Physical check

One cosine projects area; the other projects momentum. Specular reflection preserves tangential momentum.