Question

If critical angle is 45 degree the refractive index will be

Answer 1

depends on the refrence material.
solving for air as medium:
1÷ų=sin(45)
1/ų=1/(2)^1/2
ų=(2)^1/2

Answer 2

Refractive index ,$\bold{n = \sqrt 2}$

Explanation:

This is a case of Total Internal Reflection, here the relation between critical angle (θc) and refractive index (n) is given as,

$\theta_c = sin^{-1} \left( \frac{1}{n} \right)$

$\sin\theta_c = \frac{1}{n}$

Given, $\theta_c = 45 \textdegree$

$\sin 45 \textdegree = \frac{1}{n}$

$\frac{1}{\sqrt 2} = \frac{1}{n}$

$n = \sqrt 2$

So, Refractive index ,$n = \sqrt 2$