Q.What is optical path? Obtain the equation for optical path of a medium of thickness $d$ and refractive index $n$.

The optical path of a medium is defined as the distance $d'$ that light would travel in vacuum in the same time that it actually travels a (shorter) geometric distance $d$ through the medium. If light of speed $v=c/n$ takes time $t=d/v$ to cross the medium, then in that same time $t$ it could have travelled a distance $d'=ct=c(d/v)=nd$ in vacuum, where its speed is $c$. So the optical path is simply $d'=nd$. Since $n>1$ for every real transparent medium, the optical path $d'$ is always greater than the actual geometric path $d$ -- inserting a slab of glass into a light beam effectively lengthens the path the light 'would have' taken in vacuum by an amount $(n-1)d$, even though the …