A ray of ligh is incident normally on one of the faces of right
angled isosceles prism as shhown above. It undergoes total
internal reflection from hypotenuse. Which on of the
following is the minimum refractive index of the material of
the prism?

Explanation

Given prism is `45^(@)` isosceles prism and hence angle of incident on glass air interface `theta = 45^(@)`.
With the given ray diagram what we can say is that critical angle for this glass and air interface is less than or at the most equal to `45^(@)`. Hence, we can write the following:
`sin^(-1)((1)/(mu))le45^(@)`
`rArr" "(1)/(mu)lesin 45^(@)`
`rArr" "muge(1)/(sin 45^(@))`
`rArr" "mu ge sqrt2`