Obtain the equation for optical path of a medium of thickness d and refractive index n.

Explanation

(i) Consider a medium of refractive index n and thickness d. Light travels with a speed v through the medium in a time t. Then
` t = d/t , t = d/v`
(ii) In the same time, light can cover a greater distance d in vacuum as it travels with greater speed c in vacuum.
` c = (d')/(t)` rewritten as, ` t = (d')/(c)`
(iii) As the time taken in both the cases is the same, then
` (d')/(c) = d/v`
for the optical path d', d' `= c/v d `
As , ` c/v` n, The optical path d' is,
ď = nd
(v) As n is always greater than 1, the optical path d' of the medium is always greater than d.