Question

Consider the bending of light by the gravitation of the Sun as described by Newtonian physics. Light of frequency f passes at a distance d from the center of the Sun, which has a mass M. Show that the bending angle of the light is proportional to M/d.

Answer 1

Although the mass m of a photon is zero, if you use Newton's law of gravity with an m term in it and divide by m to get the acceleration towards the sun, the m's cancel out. Compute the integrated impulse to a photon as it passes by the sun at nearest distance d from the center.

I get something like

(G M/cd) cos^3 theta d(sin theta) = (GM/cd)cos^4theta d theta
integrated from theta = -pi/2 to pi/2

M is the solar mass and c is the speed of light

That equals the momentum change toward the sun as the photon passes by. Divide by the forward photon momentum h f/c to get the angular deflection. f is the frequency and h is Planck's constant.

The deflection is proportional to GM/d

This will not give you the right answer; you need Einstein's General Relativity theory for that.