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:

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

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

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

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

answer is B.

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Detailed Solution

Radiation pressure P is the force exerted by electromagnetic wave on unit area of the surface. I.e, the rate of change of momentum per unit area of the surface.
Momentum per unit time per unit area is $\frac{intensity}{speed of wave}$ = $\frac{I}{C}$
Change 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 $\frac{I}{C} & \frac{2 I}{C}$