It is often useful to work with the azimuthal angle γ, which is defined as the angle between the plane-of-vibration and the plane-of-incidence. Thus for linearly polarized light,

Figure P.4.69 is a plot of γ_r versus θ_i for internal and external reflection at an air€“glass interface (n_gα = 1.51), where γ_i = 45°. Verify a few of the points on the curves and in addition show that 

Figure P.4.69

(4.92) tan y; = [Eoi]1/[E0;] tan y, = [Eo]1/[Erlu tan y, = [E]1/[Er] (4.93) (4.94) and tan y, cos (0; 0,) tan yi (4.95) cos (0; + 0,)