We have to prove that for a plane wave at normal incidence on a plane surface the radiation pressure on the surface is equal to the energy density in the beam outside the surface; and that this relation holds no matter what fraction of the incident energy is reflected.
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Solution: Click For PDF Version Let the intensity of the incident plane wave be I. It is given that it falls on a plane surface at normal incidence. Let f be the fraction of the intensity of the incident radiation that is absorbed. The intensity of the reflected wave will therefore be .
The energy density in the beam outside the plane surface will be the
sum of energy density in the incident component of the plane wave,
which is
, and the energy density in the reflected component of the wave,
which is
 .
Therefore, the energy density in the beam outside the plane surface
will be
 .
We have
calculated in problem 566.
Problem 41.41 (RHK) that the radiation pressure on an object that
absorbs a fraction f of the incident radiation falling normally on
it and reflects fraction
Therefore, the total energy density outside the plane surface will be equal to the radiation pressure on the surface, irrespective of the fraction f.
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is