Relative Refractive Index and Absolute Refractive Index

Let light travel from air to medium 1. If c and v₁ are the velocities of light in these media, the refractive index of medium 1 with respect to air, or the absolute refractive index of medium 1 is given by

Similarly, when light travels from air to medium 2, we can write

Dividing equation (ii) by equation (i) we get

Thus the relative refractive index between a pair of media is the ratio of their absolute refractive indices. While the absolute refractive index of any material medium is always greater than unity, its relative refractive index may be greater or lesser than unity.

Practical Examples of Refraction

Relation between Real and Apparent Depths

The apparent depth of an object lying deeper in an optically denser medium appears to be lesser than its actual depth, due to refraction at a plan surface. This can be seen as follows.

Real and Apparent

Consider a ray of light incident on XY, normally along OA, it passes straight along OAA^l. Consider another ray from O (the object) incident at an angle i on XY, along OB. This ray gets refracted and passes along BC. On producing this ray BC backwards, it appears to come from the point I and hence AI represents the apparent depth, which is less than the real depth AO.

When angles are small, B lies close to A such that

OB ~ OA

IB ~ AI

Now, the apparent shift in the position of the object

O = AO - AI

• Its due to this reason that water tank appears shallower on account of refraction of light.

• Sun is visible to us before actual sunrise and after actual sunset due to atmospheric refraction of light.

Rays from sun (S) entering the earth's atmosphere travel from rarer to denser medium. This results in the rays bending towards the normal and appears to come from S₁, the apparent position. Therefore sun appears above the horizon. It is for the same reason it continues to be seen a few minutes after it actually sets. Hence the day becomes longer by about 4 minutes due to refraction effect.

• The twinkling effect of a star is due to atmospheric refraction. As the refracting media are not steady, the rays bend through fluctuating masses of air in motion and this causes fluctuations in the apparent position of the star and hence gives the twinkling effect.