Question

A light beam inside a container of some liquid hits the surface of the liquid/air interface. Depending on the angle, the light beam may or may not be able to get out into the air medium. At what angle will the beam of light be totally reflected back into the liquid in the container

Answer 1

Answer:

Following are the solution to the given question:

Explanation:

Applying the Snell Law:

when is the liquid's refractive index, is the air's refractive index.  

the liquid's refractive index,   the air's index of refraction.

It is the limiting case when , Inside the interphase of two mediums, light is scattered. Thus,

$n_l \sin \theta_l = n_a \sin 90^\circ = n_a$

$\theta_l = \arcsin \dfrac{n_a}{n_l} =\arcsin \dfrac{1}{1.38} = 46.4^\circ$

From  the incident angles $\theta_l$ is greater than 46.4°, that is the light reflected back into the liquid.