Physics

Dispersion of Light

Rainbow

Physics
NEET UG
Version 1Updated 22 Mar 2026

A rainbow is a meteorological phenomenon that is caused by reflection, refraction, and dispersion of light in water droplets resulting in a spectrum of light appearing in the sky. It takes the form of a multicoloured arc. Rainbows caused by sunlight always appear in the section of sky directly opposite the sun. The most common type of rainbow, the primary rainbow, is formed by light undergoing one…

Quick Summary

A rainbow is a natural optical phenomenon caused by the interaction of sunlight with atmospheric water droplets. It involves three key processes: dispersion, refraction, and total internal reflection.

White sunlight, a mixture of colors, first enters a raindrop and undergoes refraction, splitting into its constituent colors (dispersion) because each color bends at a slightly different angle. The light then travels to the back of the droplet, where it undergoes total internal reflection, bouncing back inside.

Finally, it exits the droplet, undergoing a second refraction, further separating the colors and directing them towards the observer. The primary rainbow, the brighter one, results from one internal reflection, showing red on the outside and violet on the inside, with an angular radius of about 42circ42^circ.

The secondary rainbow, fainter and larger, results from two internal reflections, with colors reversed (violet outside, red inside) and an angular radius of about 51circ51^circ. For a rainbow to be seen, the sun must be behind the observer, and water droplets must be in front.

Each observer sees a unique rainbow, as it's an optical effect, not a physical object.

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Key Concepts

Dispersion and Refractive Index

Dispersion is the fundamental reason why we see colors in a rainbow. It arises because the refractive index…

Total Internal Reflection (TIR) in Rainbow Formation

TIR is crucial for sending the dispersed light back towards the observer. After the first refraction and…

Angular Deviation and Rainbow Angles

The specific angular positions of the primary and secondary rainbows are determined by the total angular…

  • Primary Rainbow:1 TIR, Red outside (approx42circapprox 42^circ), Violet inside (approx40circapprox 40^circ), Brighter.
  • Secondary Rainbow:2 TIRs, Violet outside (approx54circapprox 54^circ), Red inside (approx51circapprox 51^circ), Fainter.
  • Phenomena:Refraction, Dispersion, Total Internal Reflection.
  • Observation:Sun behind observer, rain in front. Center at anti-solar point.
  • Critical Angle:sinθc=nairnwaterapprox11.33approx48.75circsin \theta_c = \frac{n_{\text{air}}}{n_{\text{water}}} approx \frac{1}{1.33} approx 48.75^circ.
  • Alexander's Dark Band:Dark region between primary and secondary rainbows (approx42circ51circapprox 42^circ - 51^circ) due to lack of scattered light.

For Primary vs. Secondary Rainbows: Primary: Pretty (Brighter), Proper (ROYGBIV), Precise (1 TIR), Positive angle (Red 42circ42^circ outer). Secondary: Subdued (Fainter), Switched (VIBGYOR), Second (2 TIRs), Superior angle (Violet 54circ54^circ outer).

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