(a) Derive an expression for the total shift in photon wavelength after two successive Compton scatterings from electrons at rest. The photon is scattered by an angle θ1, in the first scattering and by θ2 in the second.
(b) In general, is the total shift in wavelength produced by two successive scatterings of an angle θ/2 the same as by a single scattering of θ? If not, are there any specific values of θ, other than θ = 0o, for which the total shifts are the same?
(c) Use the result of part (a) to calculate the total wavelength shift produced by two successive Compton scatterings of 30.00 each. Express your answer in terms of h/mc.
(d) What is the wavelength shift produced by a single Compton scattering of 60.0o? Compare to the answer in part (c).