Rainbow Formation: The Physics Behind Nature's Colour Arc

A rainbow is a curved band of colours you see when sunlight passes through raindrops in the air. White sunlight looks plain, but it is actually a mix of seven colours: violet, indigo, blue, green, yellow, orange and red. When light enters a raindrop, bends, reflects inside the drop and bends again while leaving, the colours separate and spread into an arc.

Rainbows matter because they show three important ideas of light in one scene: refraction, internal reflection and dispersion. The same ideas explain how a prism splits light and why a diamond sparkles.

Key Concepts

Refraction is the bending of light when it moves from one medium to another, such as from air into water, because its speed changes. Dispersion is the splitting of white light into colours because each colour bends by a slightly different amount. Total internal reflection is the complete reflection of light inside a denser medium when it hits the boundary at an angle larger than the critical angle. For water the refractive index is about 1.33, meaning light travels 1.33 times slower in water than in vacuum. Red light bends the least and violet bends the most.

• Primary rainbow: one internal reflection inside the drop, red on the outer edge at about 42 degrees from the antisolar point.
• Secondary rainbow: two internal reflections, colours reversed, seen at about 51 degrees and fainter.
• Antisolar point: the point directly opposite the Sun from your eyes, centre of the rainbow arc.

How It Works

1. A sunbeam enters the front surface of a spherical raindrop and refracts, splitting into colours.
2. The light travels to the back of the drop and reflects internally toward the front lower part.
3. It refracts again while exiting, bending further and separating colours more.
4. Drops at the correct angle send red light to your eye at 42 degrees and violet at 40 degrees, so you see bands.
5. Millions of drops together form the full arc, each drop contributing one colour to one position.

Worked Example

Light enters a raindrop from air. The angle of incidence at the surface normal is 60 degrees. The refractive index of water for red light is 1.33. Find the angle of refraction inside the drop using Snells law.

Snells law: n1 sin i equals n2 sin r. Here n1 is 1.00 for air, n2 is 1.33, i is 60 degrees. So sin r equals sin 60 divided by 1.33.

sin 60 is 0.866. Divide by 1.33 gives 0.651. Therefore r equals sin inverse of 0.651, which is about 40.6 degrees. The ray bends toward the normal, as expected when entering a denser medium. Repeating with a slightly higher index for violet gives a smaller angle, proving dispersion separates the colours.

Common Misconceptions

• A rainbow is a physical object at a fixed place: Wrong. It is an optical effect depending on your position, Sun position and rain position. It moves with you.
• Only one person sees the same rainbow: Wrong. Each observer sees light from a different set of drops, so every person sees their own rainbow.
• Secondary rainbow has same colour order: Wrong. Two reflections reverse the order, so red is on the inner edge of the secondary bow.

Real-World Applications

Spectrometers use dispersion to study stars and chemicals. Photographers use the 42 degree geometry to predict where a bow will appear. The same refraction rules guide lens design and atmospheric studies.

In short, a rainbow forms when sunlight refracts into raindrops, reflects once inside and refracts out, spreading colours at 40 to 42 degrees. The Sun must be behind you for a bright bow.