Question

a light ray incident obliquely passes into three media as shown in the figure the refractive index of medium 3with respect to medium 1 is

Answer 1

Let us consider that refractive index of medium 1 , $\mu_1$

from Snell's law,

$\mu_1sini=\mu_2sinr$

or, $\mu_1sin60^{\circ}=\mu_2sin45^{\circ}$

or, $\sqrt{3}\mu_1=\sqrt{2}\mu_2$....(1)

again, applying Snell's law medium 2 And medium 3 ,

or, $\mu_2sini'=\mu_3sinr'$

or,$\mu_2sin45^{\circ}=\mu_3sin30^{\circ}$

or,$\sqrt{2}\mu_2=\mu_3$......(2)

from equations (1) and (2),

$\sqrt{3}\mu_1=\mu_3$

or,$\frac{\mu_3}{\mu_1}=\sqrt{3}$

hence, refractive index of medium 3 with respect to medium 1 is √3.