# Path of light is reversible – Principle of Reversibility of light

If a ray of light travel from medium 1 to medium 2 along a certain path, it retraces the path, when it passes from medium 2 to medium 1. Thus the path of light is reversible. And this principle is known as the principle of reversibility of light.

Here we also derive the relationship equation between the refractive index values of 2 media in contact applying the concept of Principle of Reversibility of light

## Relationship between refractive index values of 2 media in contact – Application of Principle of Reversibility

Let’s derive the relationship equation between the refractive index values of 2 media in contact applying the concept of Principle of Reversibility of light.

Let’s say AB is the refracting surface separating the two media. MN is normal on AB. path of light is reversible. And this principle is known as principle of reversibility of light.

A ray of light PQ is obliquely incident at an angle i and is refracted along QR at an angle r.
Refractive index of medium 2 with respect to medium 1 is 1µ2 = sin i / sin r ………………. (1)

When a ray of light travels from medium 2 to medium 1, according to the principle of reversibility, RQ is the incident ray and QP is the refracted ray.

In this case, angle r is acting as the angle of incidence and angle i is the angle of refraction.
So, from here we can formulate the refractive index of medium 1 with respect to medium 2 in this way:
2µ1 = sin r / sin i ………………. (2)

So from (2) and (1) we get, 2µ1 = sin r / sin i = 1/(sin i / sin r) = 1/ 1µ2
=> 2µ1 = 1/ 1µ2

This is relationship between the refractive index values of 2 media in contact derived from the Principle of Reversibility of light.

Path of light is reversible – Principle of Reversibility of light
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