Question

Light enters in a glass slab of refractive index $\dfrac{3}{2}$and covers a distance of 20 cm. The optical path is
A. $40 cm$
B. $30 cm$
C. $\dfrac{{40}}{3}$ cm
D. $60 cm$

Answer 1

We can calculate the value of optical path or length of optical path by multiplying the refractive index of the medium i.e., glass slab by the distance covered by the light ray when it enters the glass slab.

Formula used:
$Optical{\text{ }}path = \mu \times d$
Where, $\mu=$ Refractive index of the medium and $d=$ Distance covered by the light ray.

Complete step by step solution:
A light enters in a glass slab whose refractive index is $\dfrac{3}{2}$. The refractive index of a medium is defined as the ratio of the speed of light in vacuum (or air) to the speed of light in that medium and it is represented by the symbol $\mu$ . The refractive index of a glass slab is $\dfrac{3}{2}$ which means that the light travels in air $\dfrac{3}{2}$ or 1.5 times faster than in glass. We can find the value $\dfrac{3}{2}$ by calculation also i.e.,
$\mu$ = $\dfrac{{speed{\text{ }}of{\text{ }}light{\text{ }}in{\text{ air}}}}{{speed{\text{ }}of{\text{ }}light{\text{ }}in{\text{ }}glass}}$
$\Rightarrow\mu = \dfrac{{3 \times {{10}^8}m/s}}{{2 \times {{10}^8}m/s}}$
$\Rightarrow\mu = \dfrac{3}{2}$

Optical path is defined as the path travelled by a light ray when it passes through an optical medium. The optical path length is obtained by multiplying the length of the path travelled by the light by the refractive index of the medium i.e., glass. We know that the length covered by the light when it enters the glass slab is 20 cm and let it be represented by d. Hence,
$Optical{\text{ }}path = \mu d$
$\Rightarrow Optical{\text{ }}path = \dfrac{3}{2} \times 20cm$
$\therefore Optical{\text{ }}path = 30cm$

Therefore, option B is correct.

Note: Kindly remember the formula of optical path because from its formula only i.e., optical path is equal to the refractive index multiplied by distance travelled by the light ray when it enters the glass slab, one can easily get the answer of this question.