In the same time that it takes a beam of light to travel a distance $d$ in a material of refractive

Question

In the same time that it takes a beam of light to travel a distance $d$ in a material of refractive index $\mu$, the beam would travel in air a distance ______ called _______

Professor PC Thomas Classes · Answer

Time taken by light to travel a distance $d$ in a medium $\frac{d}{c_{m}}$ where $c_{m}$ is the speed of light in the medium. The distance which light can travel in air during this time $$ =\mathrm{c}_{\mathrm{u}} 	imes \frac{\mathrm{d}}{\mathrm{c}_{\mathrm{m}}}=\left(\frac{\mathrm{c}_{\mathrm{u}}}{\mathrm{c}_{\mathrm{m}}}ight) \mathrm{d}=\mu \mathrm{d} $$ where $c_{a}$ is the speed of light in air. Thus a distance $d$ of a medium of $R I=\mu$ is equivalent to $\mu d$ in air and it is known as optical path length.\