How does refraction cause a rainbow?

In one line

The rule

Refraction is the bending of light as it passes from one medium to another due to a change in speed.

The main formula for refraction is: n₁ sin θ₁ = n₂ sin θ₂ where:

• n₁ = refractive index of the first medium (like air)
• θ₁ = angle of incidence (incoming angle)
• n₂ = refractive index of the second medium (like water)
• θ₂ = angle of refraction (bent angle)

Let's understand it simply

Imagine sunlight as a team of runners, all running together. When they hit a muddy field (a raindrop), some runners slow down more than others. The fastest ones (red light) slow down the least, and the slowest (violet light) slow down the most. This makes the team spread out—just like light spreads into different colors.

Now, think of a raindrop as a tiny glass ball in the sky. When sunlight enters it, it bends (refraction), bounces inside (reflection), and bends again as it comes out. Each color bends a different amount, so they come out at different angles. That’s why you see a rainbow as a curve of colors in the sky.

How it works

1. Sunlight (white light) enters a raindrop from the air.
2. As it enters, it slows down and bends (refracts) because water is denser than air.
3. Inside the drop, light reflects off the back of the drop (like a ball bouncing off a wall).
4. The light bends again (refracts) as it leaves the drop and goes back into the air.
5. Each color bends by a different amount—red bends the least, violet bends the most. This spreads the colors apart.
6. When millions of drops do this together, you see a rainbow in the sky.

The story behind it

People have wondered about rainbows for thousands of years. The first scientific explanation came from Isaac Newton in the 17th century. He used a glass prism to show that white light is made of many colors. Later, scientists explained how raindrops act like tiny prisms in the sky. Newton’s curiosity about light and color helped us understand not just rainbows, but also how light works in our daily lives.

Where you see it in real life

• After rain on a sunny day: Sunlight hits leftover raindrops in the air, making rainbows.
• Spraying water from a hose: If you spray water in sunlight, you can see a mini-rainbow.
• Dew on grass: Early morning dew can create tiny rainbows when sunlight passes through the drops.
• CDs and soap bubbles: The colors you see are also from light bending and spreading, though the process is a bit different.
• Waterfalls: Mist from a waterfall can create rainbows if the sun is behind you.
• Monsoon season: Rainbows are common when the rain stops and the sun comes out.

Why it matters

• Nature’s beauty: Rainbows show us how light works in a beautiful way.
• Science of light: Understanding rainbows helps us learn about refraction, reflection, and color.
• Optical instruments: The same rules help make lenses for glasses, cameras, and microscopes.
• Weather prediction: Seeing a rainbow can tell you where the sun and rain are in the sky.

Worked example

Let’s see how much red and violet light bend inside a raindrop:

Given: n₁ (air) = 1.0, n₂ (water) = 1.33
Angle of sunlight (θ₁) = 42°
Step 1: Write Snell’s Law      n₁ sin θ₁ = n₂ sin θ₂
Step 2: For red light, n₂ (water) ≈ 1.331
         1.0 × sin(42°) = 1.331 × sin θ₂
         sin θ₂ = sin(42°)/1.331 ≈ 0.669/1.331 ≈ 0.503
         θ₂ ≈ 30.2°
Step 3: For violet light, n₂ (water) ≈ 1.343
         sin θ₂ = sin(42°)/1.343 ≈ 0.669/1.343 ≈ 0.498
         θ₂ ≈ 29.8°
Step 4: The small difference in bending spreads the colors apart.

Common mistakes

• Thinking only reflection makes a rainbow: Both refraction and reflection are needed.
• Believing all colors bend the same: Each color bends differently—this is why we see separate colors.
• Forgetting the sun’s position: The sun must be behind you for a rainbow to appear in front.
• Assuming one raindrop makes a rainbow: Millions of drops together make the full arc.

Remember it

Rainbows happen when sunlight bends, bounces, and splits inside raindrops—making nature’s color show.