Q.What is optical path ? Write down the equation for optical path and mention what each term represents.

Optical path length is the vacuum-equivalent distance corresponding to the actual path traversed in a medium, given by $\Delta=\mu d$.

1. Definition. When light travels a geometric distance $d$ through a medium of refractive index $\mu$, it takes longer than it would to travel the same distance in vacuum (since its speed in the medium, $v=c/\mu$, is less than $c$). The optical path is defined as the distance light would have travelled in vacuum in the same time that it actually takes to traverse the geometrical path $d$ in the medium.

2. Derivation of the equation. Time taken to cross the medium:

$t = \dfrac{d}{v} = \dfrac{d}{c/\mu} = \dfrac{\mu d}{c}$

In this same time $t$, the distance light would cover in vacuum (at speed $c$) is

$\Delta = c\,t = c\times\dfrac{\mu d}{c} = \mu d$

3. Equation and terms.

$\Delta = \mu d$

where:

• $\Delta$ = optical path length,
• $\mu$ = refractive index of the medium, …