Optical Path - Practice Questions & MCQ

Optical path-

It is defined as the distance travelled by light in a vacuum, in the same time in which it travels a
given path length in a medium.

Let light cover distance t in the medium having a refractive index as $\mu_{\text {in Time }}^{\mathrm{T}}$.
So $T=\frac{t}{v}$ where $\mathrm{v}=$ speed of light in the medium
and $\mu=\frac{c}{v}$ where $\mathrm{c}=$ speed of light in the vacuum.
$\mathrm{So}^T=\frac{t \mu}{c}$

So in the same time T distance covered by light in a vacuum is

$$
l=c T=c * \frac{\mu t}{c}=\mu t
$$

So the relation between geometrical path ( t ) and optical path (I) is given as $l=\mu t$
- For two medium in contact as shown in the below figure

the optical path is equal to $\mu_1 x_1+\mu_2 x_2$
- Change in the optical path in a transparent slab

Consider the following two cases
Case I- A light cover distance $l=A B$

So the optical path in this case is $L_1=l$

Case II- Now a slab of thickness t is placed between A and B

So distance travells in slab=t
and distance travells in air $=l-t$
So the optical path in this case is $L_2=(l-t)+\mu t$
Now change in the optical path $=\Delta x=L_2-L_1=[(l-t)+\mu t]-[l]=t(\mu-1)$
I.e due to insertion of the slab the optical path is increased by $\Delta x=t(\mu-1)$