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

Last updated on April 14th, 2021 at 04:59 pm

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.

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 ** _{1}µ_{2}** = 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:** _{2}µ_{1}** = sin r / sin i ………………. (2)

**So from (2) and (1) we get, _{2}µ_{1} = sin r / sin i = 1/(sin i / sin r) = 1/ _{1}µ_{2}**=>

_{2}µ_{1}= 1/_{1}µ_{2}This is **relationship between the refractive index values of 2 media in contact** derived from the **Principle of Reversibility** of light.