Light travels in two media M _ 1 and M _ 2 with speeds 1 . 5 × 10 ^...

Relative refractive index can be found as,

$\dfrac{{\mu}_{2}}{{\mu}_{1}} = \dfrac{{v}_{1}}{{v}_{2}} = \dfrac{1 . 5}{2} = \dfrac{3}{4}$.

When the angle of incident is greater than the critical angle total internal reflection occurs. If the critical angle is ${i}_{c}$ then,

$sin{i}_{c} = \dfrac{{\mu}_{2}}{{\mu}_{1}} = \dfrac{3}{4}$

Now $tan{i}_{c} = \dfrac{3}{\sqrt{{4}^{2} - {3}^{2}}} = \dfrac{3}{\sqrt{7}}$

Therefore, ${i}_{c} = \tan^{- 1}\left(\dfrac{3}{\sqrt{7}}\right)$