An important optical effect that explains how raindrops produce rainbows is refraction.
Refraction refers to the way that electromagnetic radiation (light) changes speed and direction as it travels across the interface between one transparent medium and another.
- As light travels from a fast medium such as air to a slow medium such as water it bends toward the normal and slows down.
- As light passes from a slower medium such as water to a faster medium such as air it bends away from the normal and speeds up.
- In a diagram illustrating optical phenomena like refraction or reflection in a raindrop, the normal is a line drawn from the surface of a raindrop to its centre.
- The speed at which light travels through a given medium is expressed by its refractive index (also called the index of refraction).
- If we want to know in which direction light will bend at the boundary between transparent media we need to know:
- Which is the faster, less optically dense (rare) medium with the smaller refractive index.
- Which is the slower, more optically dense medium with the higher refractive index.
- The degree to which refraction causes light to change direction is dealt with by Snell’s law.
- Snell’s law considers the relationship between the angle of incidence, the angle of refraction and the refractive indices (plural of index) of the media on both sides of the boundary. If three of the four variables are known, then Snell’s law can calculate the fourth.
More about refraction in a raindrop
- Light rays (streams of photons) undergo refraction twice when they encounter a raindrop, once as they enter, then again as they leave.
- Once inside a raindrop, a given photon may reflect off the inside surface of a raindrop several times, but on each refraction, some light crosses the boundary back and undergoes refraction as it escapes into the surrounding air.
- Some photons never escape, instead, they are absorbed when they strike electrons within a raindrop, releasing heat that can causes evaporation.
About scattering in raindrops
Here are three related descriptions of what causes scattering when visible light strikes a raindrop:
- When light of a specific wavelength strikes the surface and enters a raindrop its subsequent path depends upon the point of impact, and the refractive indices of water and air.
- When rays of light of a single wavelength strike a raindrop at different points, scattering is primarily determined by the angles at which they enter the droplet.
- The interaction between refraction and chromatic dispersion gives rise to the appearance of rainbow colours when parallel white light rays strike various points on the surface of a raindrop.
A secondary rainbow appears when sunlight is refracted as it enters raindrops, reflects twice off the inside surface, is refracted again as it escapes back into the air, and then travels towards an observer.
- A secondary rainbow always appears alongside a primary rainbow and forms a larger arc with the colours reversed.
- A secondary rainbow has violet on the outside and red on the inside of the bow.
- When both primary and secondary bows are visible they are often referred to as a double rainbow.
- A secondary rainbow forms at an angle of between approx. 50.40 to 53.40 to its centre as seen from the point of view of the observer.
- A secondary bow is never as bright as a primary bow because:
- Light is lost during the second reflection as a proportion escapes through the surface back into the air.
- A secondary bow is broader than a primary bow because the second reflection allows dispersing wavelengths to spread more widely.
- The axis of a rainbow is an imaginary line passing through the light source, the eyes of an observer and the centre-point of the bow.
- The space between a primary and secondary rainbow is called Alexander’s band.