Chapter 24, Problem 20Q

(a)

To determine

The color of the top of the rainbow in case of a diffraction grating.

Answer to Problem 20Q

The color of the top of the rainbow in case of a diffraction grating is violet.

Explanation of Solution

Introduction:

A diffraction grating can be defined as a large number of slits which are equally spaced. Diffraction grating can be divided in two types: transmission and reflection grating.

According to Bragg’s law of diffraction:

  $d\sin \theta =m\lambda$

Here, $d$ is the distance of separation.

  $\theta$ is the angle of deviation.

  $\lambda$ is the wavelength

In case of diffraction grating, the angle of deviation is smallest from the horizontal. So, for the given values of $d$ and $m$ , the wavelength is shortest. Hence, for diffraction grating the color on the top of the rainbow is violet. As violet light is having shorter wavelength as compared to the red light.

Conclusion:

Thus, the color of the top of the rainbow in case of a diffraction grating is violet.

(b)

To determine

The color of the top of the rainbow in case of a prism.

Answer to Problem 20Q

The color of the top of the rainbow in case of a prism is red.

Explanation of Solution

Introduction:

When a ray of light is passing from one medium to another medium, then the measurement of the bending of the light ray can be defined as refractive index or index of refraction.

A prism is made up of glass which is a transparent material. Now, the refractive index of glass is larger for shorter wavelengths and smaller for longer wavelength. From the horizontal direction, red light will appear on the top of the rainbow.

Conclusion:

Hence, the color of the top of the rainbow in case of a prism is red.