Chapter 24, Problem 5Q

To determine

To explain: The outcome of certain should be discussed.

Answer to Problem 5Q

The wavelength of light will change when Young’s double-slit experiment submerged in water.

Explanation of Solution

Introduction: Young’s double-slit helps to understand the wave theory of light. For this it used two coherent sources of the light.

The wavelength of light in a medium such as water is decreased when compared to the wavelength in air. If $\text{λ}$ is decreased, then $\text{θ}$ will also be decreased. Now, assume that $\text{m}$ and $\text{d}$ are fixed. The bright spots will appear closer together. Also, the path difference is an integer multiple of the wavelength in constructive interference.

So, $d\sin \left(\theta \right)=m\lambda$

Where,

  $m$ is an integer

  $\lambda$ is wavelength

  $d$ is a distance

This expression states that the bright spots on screen are more tightly packed together in water as compared in air.

Conclusion: The path difference is an integer multiple of wavelength in constructive interference.