Radiation Pressure — Question 3

Question 3

An oblique absorber receives a tangential radiation force

A black stationary plate of area A absorbs a vacuum beam of intensity I incident at angle theta from its inward normal. Let n point normally into the plate and t point along the incident tangential component. Ignore thermal reradiation during the measurement.

1. Find the vector force and its normal and tangential components.

2. Find the ratio of tangential to normal force at 30 degrees and compare the normal force to a perfect mirror.

Question 3 - Solution

An oblique absorber receives a tangential radiation force

(a) Method and calculation

$$\hat k=\cos\theta\,\hat n+\sin\theta\,\hat t,\quad\mathbf F=\frac{IA\cos\theta}{c}\hat k.$$$$\boxed{F_n=IA\cos^2\theta/c,\quad F_t=IA\sin\theta\cos\theta/c}.$$

(b) Interpretation and further calculation

$$\boxed{F_t/F_n=\tan30^\circ=1/\sqrt3}.$$$$\boxed{F_{n,\mathrm{abs}}/F_{n,\mathrm{mirror}}=1/2}.$$

Physical check

Absorption removes both components of incident momentum; a specular mirror reverses only the normal component.