### EXERCISE 5: CRUDE ESTIMATE OF THE IRRADIANCE VERSUS DEFLECTION ANGLE FOR A SINGLE WAVELENGTH: PRIMARY RAINBOW

Assume that the each outgoing ray produces an irradiance that is equal to I(θ)=I 0 exp[−(θ−δ)2] where here the angles are assumed to be in degrees and the implied width of this distribution is 1∘. (For simplicity, we neglect the loss of intensity during refraction and internal reflection. This is a huge oversimplification, but it allows us to focus on adding up contributions from each ray.) Sum up the contributions from rays uniformly distributed over the scaled impact parameter b~=b/R to compute the overall irradiance as a function of deflection angle for light of wavelength 400 nm. Plot the resulting irradiance distribution versus deflection angle for a single wavelength. How does this plot help explain why the rainbow is bright?