Question

A light wave falls normally on the surface of glass coated with a layer of transparent substance. Neglecting secondary reflections, demonstrate that the amplitudes of light waves reflected from the two surfaces of such a laver will be equal under the condition n' = √n, where n' and n are the refractive indices of the layer and the glass respectively.

Answer 1

Suppose the incident light can be decomposed into waves with intensity I_|| & I_⊥ with oscillations of the electric vectors parallel and perpendicular to the plane of incidence. 

For normal incidence we have from Fresnel equations

This shows that the light reflected as a fraction of the incident light is the same on the two surfaces if n' = √n.

Note:- The statement of the problem given in the book is incorrect. Actual amplitudes are not equal; only the reflectance is equal.