What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness ' h ' in terms of the angle of incidence ' i ' and angle of refraction ' r ', if the glass slab is placed in air medium?

Solution

Physics sir · 4 steps

Find the path length inside the slab first, then the shift is just that length times sin(i-r).

1. Path inside glass. Let the ray enter at A and leave at B on the lower face. AB makes angle r with the normal, and the vertical depth is h, so AB = h/(cos r).
2. Angle with original line. Extend the incident ray straight on, without bending. It makes angle i with the normal, while AB makes angle r, so AB is turned away from it by (i-r).
3. Drop a perpendicular. The emergent ray is parallel to the incident ray. The lateral shift d is the perpendicular distance from B to the extended incident line, which is AB sin(i-r).

   d = AB sin(i-r) = (h sin(i-r))/(cos r)

4. So. The lateral shift is (h sin(i-r))/(cos r), which is option (d).

The idea to keep. For a glass slab, the path inside is h/cos r, and the shift is that path times the sine of the deviation (i-r). The ray comes out parallel, so only a sideways shift remains.

Answer from the NTA final answer key. Solution by PrepWiser.