First slide

Momentum and Radiation pressure

Question

Plane electromagnetic waves of intensity S are incident normally on a flat surface. Only a fraction f of the incident energy is absorbed. What is the radiation pressure?

Difficult

A

S/c (3 – f)
B

S/c (2 – f)
C

S/c (4 – f)
D

S/c (f – 1)

Solution

$\begin{array}{rcl} P & = & P_{absorbed light} + P_{reflected}; \\ P & = & \frac{I_{1}}{C} + \frac{2 (I - I_{1})}{C} \end{array}$
Let I₁ be the intensity absorbed, fraction
$\begin{array}{rcl} f & = & \frac{I_{1}}{I} = \frac{I_{1}}{S} \\ \Rightarrow & I_{1} = Sf \\ P & = & \frac{Sf}{C} + \frac{2 (S - Sf)}{C} \\ \Rightarrow & P = \frac{S}{C} (2 - f) \end{array}$

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