4. RAy tracing  ACross the slab

We saw that when a ray of light enters an optically denser medium, it bends towards the normal. In this section we will see what happens to the ray when it leaves the denser medium and emerges back into air. Let us consider that the source is in air at S and the ray that strikes a block of glass at the point O. The figure shown below is the same as Figure 3 in section 2; however, as our goal is to study refraction, we now only investigate the refracted component OT .

  The refracted component OT continues and meets the opposite surface of the block at P.

In absence of the block, the ray SO would have continued along OU.

The refracted ray is therefore deviated by an angle,

δ = ∠ UOM - ∠ POM

   = ∠ UOP

δ is called as the angle of deviation.

The refracted ray meets the surface of separation of glass to air at P.  Draw the normal (PQ)  to this surface at P.  The angle of incidence at this surface is ∠OPQ = u.

On refraction at this surface the ray bends away from the normal along PT.

The angle of refraction = ∠TPR = e, Applying  Snell's law:

sin u / sin e = 1/μ           Eq. 4

Note that u is the angle of incidence in the denser medium and e is the refracted angle from the slab into vacuum.  It is intuitive to note that as both OM and PQ are both normal to the rectangular slab, they are parallel. Hence

∠ r = ∠ u  ,

from Eq. 2 (Previous section) and Eq. 4,

∠ e = ∠ i  .

The emergent ray is parallel to the extended incident ray  OU.

Reciprocity in optics

We now arrive at an important principle in optics.  In the above figure, suppose the source is removed from the point S and placed at the point T. Considering the ray at the same angle of incidence  e = i , striking the rectangular slab at the point P,   on entering the slab the ray will bend according to the law :

sin e / sin u = μ   because the light is now travelling from vacuum to glass. 

That is, the ray retraces the path when the direction of the incident ray is reversed.  Similarly, the refracted ray within the slab on reaching the point O, will get refracted along  OS following the same principle. This is called as the principle of reciprocity in optics.