Tallinn University of Technology

In the recent days of frosty weather, those who visited Tallinn’s seashore may have noticed ships seemingly floating in the sky. Professor Jaan Kalda at the Tallinn University of Technology sheds light on this unusual phenomenon.

miraaž Jaan Kalda
Mirage. Illustration by Jaan Kalda

This article was published in the Estonian news portal Novaator.

When ships appear to ‘hover’ in this way, what you are seeing is a mirage: a phenomenon where light rays, instead of travelling in a straight line, are bent due to the refractive index of air varying at different altitudes. Your eye ‘thinks’ objects are in the direction from which light enters it. If the ray of light is bent, your eyes are deceived.

Mirrors provide the simplest example of this phenomenon, as they too bend (or, more precisely, refract) light. When viewed in a mirror, objects appear to be positioned at the site of their mirror image and not in their true location.

Another example can be seen in clear water in a lake or pool. If you look into the water, it appears to get shallower further away from you, when in reality it is equally deep at every point. This is because light rays travelling from the direction of your eyes refract at the surface of the water towards the water, which is an environment with a higher refractive index.

You might think that air is such a thin medium that it has no noticeable refractive effect on light. Normally, this is true, but when a ray of light comes from a distant object, then even a small angle of divergence can correspond to a large distance and be very noticeable to the eye.

There are two types of mirages

So-called inferior mirages occur when the ground (e.g., desert sand or asphalt road) is extremely hot, causing the air near the ground to also heat up. The hot air expands and thus becomes thinner than the cooler air above. As air gets thinner, its refractive index decreases, causing light to bend upwards, towards cooler air.

As a result, objects appear lower than they actually are; see Figure (a). This sometimes results in an illusion of ‘puddles’ on hot asphalt roads, which are not actually water, but a reflection of the sky: a layer of hot air can reflect light just like the surface of water.

‘Superior’ mirages occur in the opposite situation – when air near the ground is colder. This produces an opposite effect compared to inferior mirages: light rays bend downwards and objects appear to be higher than they really are; see Figure (b). This primarily occurs in winter, when the ground cools due to releasing thermal radiation; the effect is strongest on clear winter mornings, when the heat of the ground has been radiated into space throughout the night through the open sky and the sun has yet to heat the ground up.

The cool ground then also causes the lower layers of air to cool down, resulting in a so-called inversion, where temperatures are lower below than above. Such a situation is bad for human health, because it traps exhaust gases and smoke near the ground. The cold air at lower altitudes is heavier than the warmer air above and cannot move upwards.

This is called an inversion, because normally the opposite is true: temperatures are lower higher up, normally dropping by one degree over every hundred metres. Superior mirages can also occur at sea in the spring, when the water is still cold or even iced over while air warmed by the sun travels onto the sea from land.

Many will probably have forgotten the law of refraction as taught in school. In a transparent medium, such as water, glass, or air, light travels more slowly than in a vacuum, and the refractive index describes by how many times the speed of propagation decreases in a medium. Light is known to travel along the fastest path from one point to another (this is called Fermat’s principle).

For an intuitive way to understand this, imagine that light, as an electromagnetic wave, is able to ‘test’ every possible path of propagation, and the first waves of light to arrive at the destination are those that have chosen the best trajectory. The result is that light bends towards the region with the higher refractive index (lower speed of propagation).

If you wanted to reach a tree that was located a dozen steps away from the road, in deep snow, as quickly as possible, you should also take the route which ‘refracts’ towards the mounds of snow, initially moving along the road until your position is nearly perpendicular to the tree, and only then turn towards the tree and start wading through the snow.