Photons Have Momentum — Question 2

Question 2

Partial reflection and absorption contribute different momentum transfers

A normally incident beam of power $P=2.00\,\mathrm{mW}$ strikes a stationary planar coating. Power fractions are $R=.500$ specular reflection, $A=.300$ absorption and $T=.200$ unchanged forward transmission. Neglect thermal recoil. Use $c=3.00\times10^8\,\mathrm{m/s}$.

1. Derive the force on the coating.

2. Find the force and absorbed heating power.

Question 2 - Solution

Partial reflection and absorption contribute different momentum transfers

(a) Method and calculation

$$\dot p_{\mathrm{incident}}=P/c,\quad\dot p_{\mathrm{outgoing}}=TP/c-RP/c.$$$$\boxed{F=(1-T+R)P/c=(A+2R)P/c}.$$

(b) Interpretation and further calculation

$$\boxed{F=8.66667\times10^{-12}\,\mathrm N}.$$$$\boxed{P_{\mathrm{heat}}=AP=.600\,\mathrm{mW}}.$$

Physical check

Reflected photons reverse their normal momentum; transmitted photons with unchanged direction and energy transfer none in this model.