Photon Momentum and Radiation Pressure.

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

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

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

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

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

There is no flux intensity given in the question