Question

A beam of white light is incident normally on a plane surface absorbing 70$\%$ of the light and reflecting the rest. If the incident beam carries 10 W of power, find the force exerted by it on the surface.

Answer 1

Power = 10 W [P-Momentum]

$\lambda =\frac{h}{p}\text{or}P=\frac{h}{\lambda }$

$\text{or}\frac{P}{t}=\frac{h}{\lambda t}$

$\text{E}=\frac{hc}{\lambda }$

$\text{or}=\frac{E}{t}=\frac{hc}{\lambda t}\text{Power (W)}$

$W=\frac{Pe}{t}$

$\text{or}=\frac{W}{e}=\frac{P}{t}\text{(force)}$

$\text{or}\text{Force}=\frac{7}{10}\left(\text{absorbed}\right)+2\times \frac{3.3}{10}\text{(reflected)}$

$=\frac{7}{10}\times \frac{W}{c}+2\times \frac{3}{10}\frac{W}{c}$

=$\frac{7}{10}\times \frac{10}{3\times {10}^8}+2\times \frac{3}{10}\times \frac{10}{3\times {10}^8}$

= $\frac{13}{3}\times {10}^{-8}=4.33\times {10}^{-8}N$