Question

What must be the index of refraction of the liquid such that the direction of the light entering the liquid is not changed?

A ray of light is travelling in glass and strikes a glass/liquid interface. The angle of incidence is 51.0°, and the index of refraction of glass is n = 1.50.

Answer 1

The refractive index of liquid must be `=1.50`

Explanation:

If a ray of light is traveling from glass to liquid, we know that

`sin\theta_l = \frac{n_g}{n_l}\sin\theta_g` ......(1)

where `theta_l and theta_g` are angel of refraction and angle of incidence and `n_l and n_g` are respective refractive indices.

It is required that the direction of light entering liquid must not change. This implies that `theta_l = theta_g`. If we insert this equality in the expression (1), we obtain

`n_l = n_g=1.50`
This is independent of angle of incidence.