Question

A beam of light is incident from air on the surface of a liquid. If the angle of incidence is 38.0° and the angle of refraction is 26.5°, find the critical angle for total internal reflection for the liquid when surrounded by air.

Answer 1

The critical angle for total internal reflection for the liquid when surrounded by air is 46.8 degrees.

Step-by-step explanation:

Given that,

Angle of incidence, i = 38°

Angle of refraction, r = 26.5°

Firstly, we will find the refractive index of the liquid. It can be calculated using Snell's law as :

`n=(\sin i)/(\sin r)\\\\n=(\sin (38))/(\sin (26.5))\\\\n=1.37`

The relation between refractive index and critical angle for total internal reflection for the liquid is given by :

`\sin\theta_c=(1)/(n)\\\\\sin\theta_c=(1)/(1.37)\\\\\theta_c=46.8^(\circ)`

So, the critical angle for total internal reflection for the liquid when surrounded by air is 46.8 degrees.