Force exerted by a beam of light

[Mr confusion]

Homework Statement

FORCE on a sphere due to a beam of light
a beam of light(thick enough to shower the whole sphere) is falling horizontally on a perfectly reflecting sphere of intensity I. what is the force exerted by this light beam on the sphere?

Homework Equations

p=U/c, area element=a^2 sin theta d theta d phi



3. The Attempt at a Solution
while solving this, i get 4 sines , 1) for area element on sphere R^2 sin theta dtheta dphi
2)for momentum component of photon in radial direction
3)for dot product of intensity with area element to get energy incident on area element normally.
4) for net component of forces along horizontal direction. (vertical ones get canceled out due to symmetry).
but my book shows 3 sines and 1 cos.and the answer is thus coming different(pi R^2 I/c) can anyone show me where i am going wrong? thanks.

 

[NateD]

The attempt at a solution is incorrect. The correct approach to solve this problem is to use the principle of conservation of momentum. Since the beam of light is incident on the sphere with intensity I, it will exert a force on the sphere. The force can be calculated by using the equation F = I/c, where c is the speed of light. Therefore, the force exerted by this light beam on the sphere is equal to I/c.