Light in Nature: Apparent Depth, Mirages, Shimmering and Rainbows

Nature's optics lab

On a hot July day, the highway ahead seems to have a puddle that disappears as you drive closer. A swimming pool looks shallower than it really is. After a summer storm, a rainbow arches across the sky. On a cold January morning, two bright spots called sun dogs glow on either side of the Sun. Every one of these is explained by the properties of light you have learned: refraction, reflection, total internal reflection and dispersion.

1. Apparent depth

Light from a coin at the bottom of a pool travels up through the water. At the surface it passes into air (faster), so it bends away from the normal. Your brain traces the rays back in straight lines, and they seem to come from a point higher than the coin. Objects under water look shallower (and closer) than they really are.

When you look straight down (at small angles), the apparent depth is about:

apparent depth ≈ real depth ÷ n

For water (n = 1.33), things look about three-quarters as deep as they really are. When you look at a slant, they look even shallower. This is why a pool can be deeper than it looks, and why a person spear-fishing must aim below where the fish appears.

2. Shimmering and twinkling

The index of refraction of air depends on its temperature: warm air is less dense and has a slightly lower n than cool air. Above a hot road, a barbecue or a candle flame, pockets of warm and cool air rise and mix constantly. Light passing through is bent a little one way, then the other, and the bending changes from moment to moment, so objects behind seem to shimmer or waver.

Stars twinkle for the same reason: their light passes through layers of moving air of different temperatures. Planets usually twinkle less, because they appear as tiny discs rather than points.

3. Mirages

A mirage is an image formed when light is bent by layers of air at different temperatures.

• Inferior mirage (the "wet road"). On a hot day, the air just above the pavement is much hotter than the air above it. Light from the sky (or from a tree or car ahead) heading down towards the road passes into warmer air with a lower n, so it keeps bending away from the normal, curving upward before it reaches the road (if it meets the hot layer at a shallow enough angle, it is turned completely around, much like total internal reflection). Your eye traces the light back in a straight line, so you see an image of the sky below the road: it looks like a shiny puddle. The puddle "moves away" as you drive towards it.
• Superior mirage. When warm air lies over very cold water or ice, the bending goes the other way and distant objects appear raised above where they really are, sometimes upside down or stretched. These are seen over the Great Lakes on some spring and summer days and over the sea ice of the Arctic.

4. Rainbows

A rainbow needs sunlight behind you and raindrops in front of you. In each drop:

1. Sunlight refracts as it enters the drop. Because of dispersion, violet bends slightly more than red, so the colours begin to separate.
2. The light reflects off the back of the drop.
3. It refracts again as it leaves, spreading the colours further.

The light leaves each drop concentrated at about 42° (red) to 40° (violet) from the direction the sunlight was travelling. So you see red light coming from drops that are 42° from the point directly opposite the Sun (the antisolar point, where the shadow of your head is), and violet from drops at 40°. That is why the rainbow is a circular arc centred on your shadow, with red on the outside and violet on the inside. If the Sun is higher than 42° above the horizon, the whole bow is below the horizon, so rainbows are seen mostly in the morning or late afternoon.

Sometimes a fainter secondary rainbow appears outside the first, at about 51°, with its colours reversed. Its light reflects twice inside each drop.

5. Halos and sun dogs

On very cold days, tiny six-sided ice crystals float in the air. Light refracting through them is bent by about 22°, producing a ring of light around the Sun or Moon called a 22° halo. When flat, plate-shaped crystals drift with their faces horizontal, the light collects into two bright spots on either side of the Sun, about 22° away: sun dogs (also called parhelia). They are a common sight during a Canadian winter, especially when the Sun is low.