The 42° Rainbow
All scenes › Chapter 3 The secret of 42 degrees
Light bunches at 42°
Light piles up near the largest angle
View in 3DThe angle where light piles up
Here are the directions of rays that entered at evenly spaced heights. No ray leaves at more than 42°, and just below 42° the rays are packed tightly together. The yellow bars count the rays in each slice 2° wide. The slice from 40° to 42° collects about 4 times as much light as the others. That is why light from this angle looks especially bright.
Why?Where the angle is at its largest, changing the height a little hardly changes the angle at all. It is like a ball thrown straight up, which seems to pause for a moment at the top. So a lot of light entering around that height leaves at almost the same angle and piles up in one place.
Learn moreIn 1637, René Descartes worked out the path of ray after ray through a raindrop and found this angle. That is why the ray where the most light gathers is called the Descartes ray. The bars were calculated from 6,000 rays entering at evenly spaced heights across a slice of the drop.
- Angle where most light gathers
- 42°
- Rays between 40° and 42°
- about 15%
- Rays between 10° and 12°
- about 3.5%
calculated from the refractive index of water (IAPWS, 20 °C) and the laws of refraction and reflection
View this scene in 3D →Read more
More in the series
The numbers come from the refractive index formula for water (IAPWS 1997) and the laws of refraction (Snell) and reflection (Fresnel). In the 3D view, the raindrop and the spreading of colors inside it are drawn larger so you can see them.