This is a two part answer. A ray of light impinges at an angle of incidence i on

Question

This is a two part answer.

A ray of light impinges at an angle of incidence i on the surface of a transparent slab of thickness d. The material of the slab has index of refraction n.

A) Show that the ray emerges on the other side of the slab is parallel to the incident ray.

B) Derive an expression giving the lateral displacement of the emergent ray from the incident one in terms of i (angle of incidence), d (thickness), and n (index of refraction).

Explinations are greatly appreciated.

Thank you.

Explanation / Answer

From Snell's law, the refracted angle is given by

sin(i) / sin(r) = nr/ni.

It appears from your question that ni = 1 and nr = n

sin(i) / sin(r) = n

sin(r) = sin(i) / n

The lateral displacement is given by

?/d = tan(r)

? = d*tan(r)

If sin(r) = x, then tan(r) = x/?[1 - x

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