Q. 25

Expert-verified
Found in: Page 452

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# A light wave has a 670 nm wavelength in air. Its wavelength in a transparent solid is 420 nm. a. What is the speed of light in this solid? b. What is the light’s frequency in the solid?

Part a

The speed of light in the transparent solid is .

Part b

The frequency of the light in the transparent solid is .

See the step by step solution

## Given information

The wavelength of light in air .

The wavelength of light in transparent solid is .

## Part a

The speed of light in a material is given by .

Where is the speed of light in a vacuum and the refractive index of the material.

The refractive index is also given as

where, is the wavelength of light in a vacuum and is the wavelength of light in the material.

Here the material is transparent solid.

From (1) and (2)

Therefore, the speed of light in this solid is .

## Part b

The relation between speed, wavelength, and frequency of the wave is given by .

The light’s frequency in the transparent solid is

Therefore, the frequency of the light in the transparent solid is .