Quick answer: A rainbow forms when sunlight is refracted and dispersed as it enters raindrops, internally reflected at the back of each drop, and refracted again as it comes out. To see one, the Sun must be behind you and there must be raindrops in front of you. A primary rainbow (one internal reflection) has red on the outside. A fainter secondary rainbow (two internal reflections) appears above it with the colours in reverse order.
After a rain shower, when the Sun comes out, a curved band of colours sometimes appears in the sky. A rainbow is not an object in the sky: it is an optical effect produced by millions of tiny raindrops, each of which acts like a small prism.
Sometimes a fainter second rainbow appears above the main one, with its colours reversed.
In CBSE Class 10 Science, Chapter 10 (The Human Eye and the Colourful World), how a rainbow is formed and the conditions needed to see one are frequently asked board exam questions.
What You Will Learn
- What a rainbow is
- The two conditions needed to see a rainbow
- The three steps inside a raindrop: refraction and dispersion, internal reflection, and refraction again
- How a primary rainbow differs from a secondary rainbow
- What Alexander's dark band is
- Why a rainbow looks like an arc, and when it can look like a full circle
1. What Is a Rainbow?
Definition: A rainbow is a natural spectrum that appears in the sky after a rain shower. It is caused by the dispersion of sunlight by tiny water droplets present in the atmosphere.
Each raindrop acts like a tiny prism: it splits white sunlight into its seven colours, VIBGYOR (violet, indigo, blue, green, yellow, orange, red).
2. Conditions for Seeing a Rainbow
Two conditions must both be true:
- The Sun must be behind the observer.
- There must be raindrops or water droplets in front of the observer, in the opposite direction to the Sun.
This is why rainbows are usually seen in the morning or evening, when the Sun is low, and never when you look towards the Sun.
3. How a Rainbow Forms Inside a Raindrop
sunlight
----------> ( drop )
1. refraction + dispersion
at the front surface
2. internal reflection
at the back surface
3. refraction as light
comes out again
<---------- colours spread out
to observer (red at about 42°,
violet at about 40°)
Step 1: Refraction and dispersion (entering the drop). White sunlight enters the raindrop and passes from air into water. It slows down and bends towards the normal. Different colours bend by different amounts, so the light splits into its colours. Violet bends the most and red bends the least.
Step 2: Internal reflection (at the back of the drop). The coloured light travels to the back surface of the drop and is reflected inside the drop.
Step 3: Refraction (leaving the drop). The reflected light reaches the front surface again and passes from water into air. It bends away from the normal and the colours spread out further, travelling towards the observer.
Important: The reflection inside the raindrop is called internal reflection. It is not total internal reflection: the angle at the back of the drop is less than the critical angle, so some light passes out of the drop there and only part of it is reflected back.
4. Primary vs Secondary Rainbow
| Feature | Primary rainbow | Secondary rainbow |
|---|---|---|
| Internal reflections in each drop | One | Two |
| Colour on the outer edge | Red | Violet |
| Colour on the inner edge | Violet | Red |
| Approximate angle from the observer's line of sight | About 40° (violet) to 42° (red) | About 50° (red) to 54° (violet) |
| Width of the band | Narrower, about 2° | Wider, about 3° to 4° |
| Brightness | Bright | Fainter, because some light escapes at each extra reflection |
| Position | Lower in the sky | Higher in the sky, above the primary |
Alexander's Dark Band
The region of sky between the primary and secondary rainbows looks darker than the rest of the sky. This is because very little reflected light from the raindrops reaches the observer from that direction. This darker band is called Alexander's dark band.
5. Why Is a Rainbow Shaped Like an Arc?
- Light of each colour reaches the observer at a fixed angle from the line joining the Sun, the observer's eye and the centre of the rainbow (about for red in a primary rainbow).
- All the raindrops that send a particular colour to your eye lie on a cone with your eye at its tip, so each colour forms a circle.
- From the ground, the lower part of this circle is hidden below the horizon, so we see only an arc.
- From an aeroplane or a high mountain, with raindrops below as well as above, it is possible to see the rainbow as a full circle.
6. Summary Table
| Step | Where it happens | What happens |
|---|---|---|
| Step 1 | Front surface, as light enters the drop | Refraction and dispersion |
| Step 2 | Back surface, inside the drop | Internal reflection |
| Step 3 | Front surface, as light leaves the drop | Refraction |
7. Exam Tips and Common Mistakes
Exam Tip: When asked how a rainbow is formed, mention all three processes: refraction, dispersion and internal reflection. A neat labelled diagram of a raindrop earns extra marks.
Exam Tip: Always state the condition that the Sun must be behind the observer.
Common Mistake: Saying that a secondary rainbow has red on the outside. In a secondary rainbow, the colour order is reversed: violet is on the outside and red is on the inside.
Common Mistake: Writing "total internal reflection" for the reflection inside a raindrop. The correct term is internal reflection.
Frequently Asked Questions
How is a rainbow formed?
Sunlight is refracted and dispersed as it enters raindrops, internally reflected at the back of each drop, and refracted again as it comes out, which spreads the colours across the sky.
What are the conditions for seeing a rainbow?
The Sun must be behind the observer, and there must be raindrops or water droplets in front of the observer.
What is the difference between a primary and a secondary rainbow?
A primary rainbow is formed by one internal reflection and has red on the outside. A secondary rainbow is formed by two internal reflections, is fainter and has the colour order reversed.
Why is a secondary rainbow fainter?
At each reflection inside the drop, some light escapes, so after two reflections less light reaches the observer.
What is Alexander's dark band?
It is the darker region of sky between the primary and secondary rainbows.
Is total internal reflection responsible for rainbows?
No. The reflection inside a raindrop is ordinary internal reflection, not total internal reflection.