Question

A laser beam in air is incident on a liquid at an angle of 40.0 degrees with respect to the normal. The laser beam's angle in the liquid is 22.0 degrees. What is the liquid's index of refraction?

Answer 1

Concepts and reason

The main concepts required to solve this problem are the ray of incident, refraction, Snell’s law, and refractive index

Initially, write the equation for the Snell’s law. Use this equation of Snell’s law and calculate the refractive index of the liquid.

Fundamentals

The equation for the Snell’s law is,

Here, is the refractive index of the first medium is the refractive index of the second medium, is the angle of the incident ray, and r is the angle of refracted ray.

The equation for the Snell’s law for the interface between the mediums air and the liquid is,

Here, is the refractive index of the air, is the refractive index of the liquid, is the angle of the incident laser beam, and r is the angle of the refracted laser beam in the liquid.

Rearrange the above equation for.

The equation for the refractive index that derived in above step1 is,

Substitute 1 for , for, and for in above equation.

Ans:

The refractive index of the liquid is 1.715.