Dispersion and Rainbow Formation

~8 min read

In 30 seconds

Dispersion: Splitting of white light into seven colours by a prism — VIBGYOR. Cause: refractive index varies with wavelength.
Order: Red bends least (longest λ), violet bends most (shortest λ).
Rainbow: Sunlight refracted, internally reflected and refracted again inside raindrops. Primary at 42°, secondary at 51°.

White light is a packet of seven colours that a prism unwraps. CDS/OTA tests the order of VIBGYOR, scattering and the geometry of rainbows.

Dispersion by Prism

Newton (1666) showed that a glass prism splits sunlight into seven colours — VIBGYOR (Violet, Indigo, Blue, Green, Yellow, Orange, Red).
Reason — refractive index of glass varies slightly with wavelength. Violet is bent most; red is bent least.
The band of colours is called a spectrum.
Passing the spectrum through an inverted prism recombines it into white light.

Rayleigh scattering: intensity ∝ 1/λ⁴. Shorter wavelengths scatter more.
Sky is blue — blue light from the Sun is scattered the most by air molecules.
Sun appears red at sunrise/sunset — long path through atmosphere scatters away blue, leaving red.
Clouds are white — water droplets are larger than wavelength; all colours scatter equally (Mie scattering).

Sunlight enters a raindrop → refracts → reflects internally off the back → refracts again on exit.
Primary rainbow: one internal reflection. Red on outer edge, violet on inner. Angle ~42°.
Secondary rainbow: two internal reflections. Order reversed (red inside, violet outside). Angle ~51°. Fainter than primary.
Observer must have Sun behind and rain in front. Maximum visibility when Sun is low.

Q: In a rainbow, which colour appears on the outer edge?

(a) Violet (b) Blue (c) Green (d) Red

Answer: (d) Red — in the primary rainbow, red is outermost.

Q: Sky appears blue due to:

(a) Reflection (b) Refraction (c) Dispersion (d) Scattering of light

Answer: (d) Rayleigh scattering — blue is scattered most.

Q: Sun appears red at sunset because:

(a) Sun is closer (b) Longer atmospheric path scatters blue light away (c) Reflection by clouds (d) Dispersion in atmosphere

Answer: (b) Long oblique path scatters blue; red reaches the eye.

Q: In a prism, which colour deviates the least?

(a) Violet (b) Blue (c) Yellow (d) Red

Answer: (d) Red — least bent.

CDS/OTA-pattern items on Dispersion and Rainbow Formation with answer keys and explanations.

Why are danger signals red?

Red has the longest wavelength of visible light and is scattered least by fog, dust and rain — visible from the greatest distance.

Why is the sky not violet, since violet scatters even more than blue?

Two reasons — sunlight has less violet than blue; and the human eye is more sensitive to blue than violet.

Can a rainbow be a complete circle?

Yes — from an aeroplane or hilltop, you can see a full circular rainbow because there is no horizon cutting it off.