Chapter 16: Q. 50 (page 453)

A helium-neon laser beam has a wavelength in air of 633 nm. It takes 1.38 ns for the light to travel through 30 cm of an unknown liquid. What is the wavelength of the laser beam in the liquid?

Expert verified

The wavelength of the laser beam through the unknown liquid is, $458.7 n m .$

Step by step solution

Helium-neon laser beam has a wavelength in air of $λ_{a} = 633 n m$

For an unknown liquid, the beam takes a time of $t = 1.38 n s = 1.38 \times 10^{- 9} s$

Distance travelled through the liquid, $d = 30 c m = 0.3 m$

Speed of the beam through the unknown liquid can be determined as,

$v = \frac{d}{t} v = \frac{0.30 m}{1.38 \times 10^{- 9} s} v = 2.174 \times 10^{8} m / s$

Now, the refractive index of the liquid can be obtained by,

$μ = \frac{c}{v} μ = \frac{3 \times 10^{8} m / s}{2.174 \times 10^{8} m / s} μ = 1.38$

The wavelength of the beam through the liquid is,

$λ_{l} = \frac{λ_{a}}{μ} λ_{l} = \frac{633 n m}{1.38} λ_{l} = 458.7 n m$

Unlock Step-by-Step Solutions & Ace Your Exams!

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.