Question

A rainbow ordinarily shows a range of colors. But if the water droplets that form the rainbow are small enough, the rainbow will appear white. Explain why, using diffraction ideas. How small do you think the raindrops would have to be for this to occur?

Short answer

If the droplets that form a rainbow are small enough to perform diffraction, instead of dispersion, then there will be a broadening of maxima and colors will start overlapping to give white light and the rainbow appears as white. The diameter of raindrops should be smaller than .

Step-by-step solution

Define diffraction and its essential condition

Diffraction is a physical phenomenon in which a wave bends around the corner of any obstacle or opening when the wave passes through the obstacle.

A necessary condition for the diffraction to happen with any wave is, that the width of the obstacle or dimension of the aperture should be comparable to the wavelength of the wave.

Explain rainbow appear as white and its condition.

The wavelength of visible light belongs to the range to . From a diffraction point of view, each color in the rainbow stands for maximum intensity at a certain angle which is given as-

$\theta =\frac{\lambda }{a}$

where a is the diameter of the droplets.If the diameter of drops becomes comparable to the wavelength of light then there will be a broadening of maxima and colors will start overlapping to give white light and the rainbow appears as white.

When the diameter of the droplet is comparable to the wavelength of visible light only when diffraction can happen. Hence,$\mathrm{a}\le 400\mathrm{nm}$ is the condition required.