Q. 13

An EM wave of intensity I falls on a surface kept in vacuum and exerts radiation pressure p on it. Which of the following are true?
A. Radiation pressure is I/c if the wave is totally absorbed.

B. Radiation pressure is I/c if the wave is totally reflected.

C. Radiation pressure is 2I/c if the wave is totally reflected.

D. Radiation pressure is in the range I/c < p < 2I/c for real surfaces.

Answer :

Given


Intensity of EM wave = I


Explanation:


Radiation exerts a force on a surface on which it falls, the pressure due to this force is called radiation pressure.


Now, for the surface with area A, then the energy provided is given by,



Now, the total force on the surface is dependent upon the number of photons N




Where, c is the speed of the wave, the wavelength and h is the Planck’s constant.


Now form de Broglie’s theorem for a particle,



where p is the momentum.


The momentum change of a photon when it hits the surface when the surface is totally reflective,



And when the surface is totally absorptive,



Therefore, the force is equal to the change of momentum of all the photons for the totally reflective surface is



And for totally absorptive surface is



And the respective pressures then




A real surface can be partially absorptive and partially reflective; therefore, the pressure will lie between perfectly absorptive and perfectly reflective values. Also real surfaces are more reflective than absorptive, hence


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