Finding Force Exerted by Photons on a Sphere

[cupid.callin]

I was given this question in my book …
A sphere of radius 1cm is placed in path of light of large aperture. The intensity of light is 0.5W/cm^2. The sphere completely absorbs photons falling on it. Find the force exerted by them on the sphere.
I solved the question and I have given the solution in the pic. Please have a look.

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Next there was another question given below it …
The same sphere is placed in same light but this time the sphere is not perfectly absorbing. Show that the force exerted by photons remains the same.

Well I have no idea how to prove the second one. Please someone help .

 

[sigmaro]

that is easy, but you need a little more complicated calculus.
i think that this time it is a perfectly reflecting surface (a mirror) than it will reflect photons in all directions. there will be a spherical symetry, we can consider rings which will have same reflecting angles starting from r=0 to r=R (radius of sphere)
for an arbitrary r angle that is between line that is parallel to path of photons and normal is arcsin(r/R)
the area of that ring is 2(pi)rdr
if you draw what i explained, you will see that angle of reflected photon is 2.arcsin(r/R) call this angle 2(theta)
so momentum of one of reflected photons is -(h/lambda)cos(2theta) right? i couldn't follow your notation but let's assume there are n photons per unit area
Ptotalx=int(0toR) [-2(pi)n.r.h.cos(2arcsin(r/R))/lambda]dr
that will give sum of x components of momentums of reflected photons, you need deltaP to find force
it is Pinitial-Pfinal. Pfinal is result of the integral, P initial is what you found on you paper. I am sure you will understand the concept because at you notes you have wrote that Pfinal is 0 since photons are absorbed, here it is simple not zero. But these two do never give the same result.

 

[cupid.callin]

Thanks a lot sigmaro!

I really helped ... question is solved!