Using snells law for light passing through 3 medium of different refractive indices. and also having certain amount of reflection at each surface. Can you help me find the total reflected and refracted ray relations for single wave reflection and refraction inside the surface for infinite times

Dear NS,

the bending of the ray serves to minimize the time required to get from a point A to point B. If the ray followed the unbent path shown with a dashed line, it would have to travel a longer distance in the medium in which its speed is slower. By bending the correct amount, it can reduce the distance it has to cover in the slower medium without going too far out of its way. It is true that Snell's law gives exactly the set of angles that minimizes the time required for light to get from one point to another. The proof of this fact is left as an exercise 

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