Radiation Pressure — Question 1

Question 1

A partly transmitting foil separates heating from momentum transfer

A normally incident vacuum beam carries 12 W. A stationary foil reflects fraction R=0.65, transmits T=0.20 forward, and absorbs the remainder. Both surrounding regions are vacuum; use c=3.00 times 10 to the eighth m/s.

1. Find the force from incoming minus outgoing momentum flux.

2. Find the heating rate and compare the force with that of a perfect absorber receiving the same power.

Question 1 - Solution

A partly transmitting foil separates heating from momentum transfer

(a) Method and calculation

$$F=\frac{P}{c}-\left(\frac{TP}{c}-\frac{RP}{c}\right)=\frac{(1+R-T)P}{c}.$$$$\boxed{F=5.80\times10^{-8}\,\mathrm N}.$$

(b) Interpretation and further calculation

$$\mathcal A=1-R-T=0.15,\quad\boxed{\dot Q=\mathcal AP=1.80\,\mathrm W}.$$$$F_{\mathrm{abs}}=P/c=4.00\times10^{-8}\,\mathrm N,\quad\boxed{F/F_{\mathrm{abs}}=1.45}.$$

Physical check

Reflection transfers momentum without depositing the corresponding optical energy as heat in the stationary idealization.