Prove that the force exerted on a sphere of radius $r$ by a light source of intensity $I$ is not affected even if the sphere is not perfectly absorbing.
Question 11,Photoelectric effect and wave-particle duality, Concepts of physics Volume-2 by Dr.HC Verma
The derivation for the force exerted on a perfectly reflecting sphere can be found here
A slight manipulation of eq-2.58 yields:
where $R$ and $a$ are the reflection and absorption coefficients of the sphere respectively.
Thus the final result would be:
Its clear that for $R=1$ and $a=0$, the result is as expected for a perfectly reflecting sphere.
However, coming back to the initial question, the final expression clearly varies for different values of $R$.
The momentum/force, obviously varies for different absorbing coefficients of the sphere. This is contradicting the question. Where have I gone wrong? Or is the question incorrect?