Notes on the formation of rainbows

Rainbows

The following figures can be found on pps. 109-112 in the photocopied ClassNotes.

This first figure shows how white light can be split into its component colors when it shines through a glass prism. The bending that occurs when light passes from one transparent material (air for example) into another (glass or water) is called refraction. The amount of bending depends on the wavelength of light: shorter wavelengths such as blue and violet are bent the most, longer wavelengths like orange and red are bent the least. The separation of white light into its colors by refraction is called dispersion.

The figure above shows a ray of white light striking a spherical raindrop. Some of the white light is reflected (a). The remainder (b) enters the raindrop. This light is bent (refracted) and split into colors (dispersed). Some of the colored rays of light reflect off the back inside surface of the raindrop (c). The colored rays of light emerge from the drop (where they are bend and dispersed some more) and head back, more or less, in the direction they came from (d).

Someone down at the ground (standing with the sun at their back) would see colored light coming from the raindrop. However because each of the colors exits the drop at a slightly different angle (read at 42^o, violet at 40^o, the other colors at angles between 40^o and 42^o) they would only see one of the rays from a given drop. They would see the ray that was headed straight toward their eyes. The other rays would either pass above the person's head or strike down near the person's feet.

To see red light, the person on the ground would need to look 42^o above the horizon (A). To see violet light, the person would need to look at a different raindrop, one that is lower in the sky and 40^o above the horizon (B). The person would see all the other colors coming from drops between 40^o and 42^o above the horizon.

^{Here's what the person on the ground would see. Red
light
would be visible on the outside edge of the primary rainblow.
Violet would be on the inside edge. The other colors would be in
between.}

^{Sometimes
you'll see a faint secondary rainbow above the primary rainbow.
The following figure shows how this rainbow forms.}

^{White light strikes the raindrop at a slightly different
position. The white light is again bent and separated into colors
but then is reflected twice inside the raindrop before emerging on the
front side of the drop. An observer on the ground would need to
look 53^o above the horizon to see the violet light and 50^o
to see the
red light.}

Here are both the primary and the secondary rainbow. The secondary rainbow is higher and dimmer than the primary rainbow. The order of the colors in the secondary rainbow is also reversed. Supernumerary arcs (faint bands of pink and green) are sometimes visible below the primary rainbow (we won't go into the cause of supernumerary arcs). Also the sky between the two rainbows appears darker than the rest of the sky (we won't explain that either)