Let us consider a long stack of thin dielectrics. The stack has N layers. The fi

Question

Let us consider a long stack of thin dielectrics. The stack has N layers. The first layer has a thickness t_1 and index of refraction n_1. Each layer afterwards increases thickness by delta t and index by delta n, until reaching the final layer which has thickness t_N = t_1 + (N - 1) delta t and index n_N = n_1 + (N - 1) delta n. Light is incident from air on the first surface at an angle theta from the normal of the surface, and exits the stack into air on the other side. What angle does the light emerge from the normal of the final surface?

Explanation / Answer

The angle of refraction from 1st surface becomes angle of incidence for next surface, and since finally light emerges into air, as it was incident from air only, therefore angle of emergence will be same as angle of incidence from 1st surface. Hence light emerges at same angle "theta "

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