A drop of liquid is spread over the hypotenuse of a right angled isosceles prism as shown in Fig. and a ray of light is incident normally on face `AB` of the prism. If refractive index of liquid is `sqrt(2)`, then for total internal reflection to occur, refractive index of material prism should be :

Answer

`2`

Explanation

As is clear from Fig.
for `T//R, C = I = 45^(@)`
From `(mu_(2))/(mu_(1)) = (1)/(sin C) = (1)/(sin 45^(@)) = sqrt(2)`
`mu = sqrt(2)mu_(1) = sqrt(2) xx sqrt(2) = 2`