An electromagnetic wave of intensity I falls on a surface kept in vacuum and exerts radiation pressure P on it. Choose wrong option from the following

Moderate

A

Radiation pressure is $\frac{I}{C}$ if the wave is totally absorbed
B

Radiation pressure is $\frac{I}{C}$ if the wave is totally reflected
C

Radiation pressure is $\frac{2 I}{C}$ if the wave is totally reflected
D

Radiation pressure is in the range $\frac{I}{C} < P < \frac{2 I}{C}$ for real surfaces

Solution

Radiation pressure P is the force exerted by electromagnetic wave on unit area of the surface , i.e, rate of change of momentum per unit area of the surface
Momentum per unit time per unit area is $\frac{int e n s i t y}{s p e e d o f w a v e}$ = $\frac{I}{C}$
Chnge in momentum per unit time per unit area $= \frac{Δ I}{C}$ =radiation pressure (p) momentum of incident wave per unit time per unit area $= \frac{I}{C}$
When wave is fully absorbed by the surface, the momentum of the reflected wave per unit time per unit area is zero
Radiation pressure $(P) =$ change in momentum per unit time per unit area $\frac{Δ I}{C} = \frac{I}{C} - 0 = \frac{I}{C}$
When wave is totally reflected , then momentum of the reflected wave per unit time per unit area is $- \frac{I}{C}$
Radiation pressure P= $\frac{I}{C} (- \frac{I}{C}) = \frac{2 I}{C}$ here, P lies between $\frac{I}{C} & \frac{2 I}{C}$

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