First slide

Momentum and Radiation pressure

Question

A radiation of energy E falls normally on a perfectly reflecting surface. The momentum transferred to the surface is (C=velocity of light)

Moderate

A

$\frac{2 E}{C^{2}}$
B

$\frac{E}{C^{2}}$
C

$\frac{E}{C}$
D

$\frac{2 E}{C}$

Solution

Energy of radiation $E = hv = \frac{hc}{λ}$
Momentum $P_{i} = \frac{h}{λ} = \frac{E}{C}$
$P_{r} = - P_{i} = - \frac{E}{C}$
momentum transferred = P_i - P_r
$= \frac{E}{C} - (- \frac{E}{C}) \Rightarrow \frac{2 E}{C}$

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