Question

A parallel beam of light of intensity $I$ is incident normally on a plane surface $A$ which absorbs $50 \%$ of the incident light. The reflected light falls on $B$ which is perfect reflector. The light reflected by $B$ is again partly reflected and partly absorbed and this process continues. For all absorption by $A$, absorption coefficient is $0.5$. The pressure experienced by $A$ due to light is $\frac{k I}{c}$. Find $k$. (Here, $c=$ speed of light)

Answer 1

The force experienced by $A$ is due to infinite number of incidence and reflection. The situation is shown in the diagram.

$F=\frac{I}{c}+\frac{0.5 I}{c} \times 2+\frac{0.5^{2} I}{c} \times 2+\frac{0.5^{2} I}{c} \times 2+\ldots$
$=\frac{I}{c}+\frac{2 I}{c}\left[\frac{1}{2}+\frac{1}{2^{2}}+\frac{1}{2^{3}}+\ldots .\right]$
$=\frac{I}{c}+\frac{2 I}{c} \times\left[\frac{1 / 2}{1-1 / 2}\right]=\frac{3 I}{c}$