(a) The side view to the left below shows an electron with velocity v = z skimming...

Question:

(a) The side view to the left below shows an electron with velocity v = νẑ skimming over a diffraction grating composed of a periodic array of metal strips with periodicity L. Explain why radiation is produced. Use a constructive interference argument to show that the radiation is observed at an angle θ above the horizontal at the wavelengths λ_n= (c/v − cos θ)L where n is a positive integer. This is called Smith-Purcell radiation.
(b) The side view to the right below shows an electron with average velocity v = vẑ skimming over the surface of a periodic array of permanent magnets with periodicity L. Explain why radiation is produced. Why does the radiation observed at an angle θ above the horizontal occur at the same wavelengths as in part (a)? This is called undulator radiation