Question

What is the largest index of refraction that the liquid can have, such that none of the light is transmitted into the liquid and all of it is reflected back into the glass?

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 following condition must be satisfied
Refractive index of glass `n_l < 1.50`

Explanation:

Total internal reflection occurs only when the ray of light is traveling from a denser to rarer medium.

In the problem the ray of light is traveling from Glass, having refractive index `n_g=1.50` striking the glass/liquid interface at an angle of `theta_g=51^@`, to liquid having refractive index `n_l`.

Let `theta_l` be the angle of refraction. We have the expression

`sin\theta_l = \frac{n_g}{n_l}\sin\theta_g`
For `angle theta_l` to be critical angle case, i.e., `=90^@` so that no light is transmitted into the liquid, the refractive index of liquid must be less than that of glass.

It implies that following condition must be satisfied that is `n_l < n_g`
or `n_l < 1.50`