Electricity and Magnetism - Department of Physics & Astronomy

27. A ray of light is incident upon the bottom surface of a dielectric slab asillustrated below. The index of refraction is not constant but rather asmooth, differentiable function of x, n(x) .a) Derive an expression for the angle between the trajectory and thenormal as a function of x for 0 ≤ x ≤ L (10 pts.).b) Derive an integral expression for the magnitude of the lateraldisplacement of the ray, denoted by “Δ ” in the diagram below (10pts.).c) Derive a relation between θ eand θ i(5 pts.).θ en=1Δx=Ln(x)Lxx=0yn=1θ i28. Answer briefly and to the point.