Question

Photon Momentum and Radiation Pressure.

We have seen that photons carry not only energy but also momentum, with each photon of wavelength λ carrying momentum pγ = Eγ/c = h/λ. This means that photon interactions can transfer momentum, and thus radiation exerts forces.

(a) Consider a flux F of photons all moving in the same direction. If the light lands perpendicular (i.e., directly) on a surface of area A, find an expression for the rate of energy flow onto the surface. From this find an expression for the rate of momentum deposit onto the surface.

(b) Use Newton’s laws to trivially explain why the momentum flow rate you found represents the radiation force on the surface. Then go on to show that the radiation pressure on the surface – the force per unit area – is Pr = F/c.

(c) Consider a 100 Watt lightbulb, illuminating your hand which is held at a distance of 10 cm. Estimate the size of your hand and find the radiation force on your hand. What mass object would have a weight equal to this force? Comment on the strength the radiation force in everyday circumstances.

(d) Now consider hydrogen at the surface of the Sun which has radius R. Imagine each proton, of mass mp, acted as if it cast a shadow of area σ. Without yet evaluating numbers, find an expression for the gravitational force on the proton due to the Sun. Also find an expression for the radiation force on the proton due to the Sun. Show that the ratio of these two forces is independent of distance from the Sun. Briefly explain why

There is no flux intensity given in the question

Answer 1