Fig 1. Reflection and refraction at the boundary of water and air.
Fig 2. Inferior mirage.
Fig 3. Superior mirage.
A mirage is an optical illusion arising from the refraction of light as it passes through air layers of different densities (Fig 1). In inferior mirages (Fig 2) distant objects appear to be reflected in water at their bases: this is because light rays traveling initially toward the ground have been bent upward by layers of hot air close to the surface. In superior mirages (Fig 3) objects seem to float in the air: this occurs where warmer air overlies cooler, bending rays downward.
Mirages and refraction
When rays of light pass at an angle from one transparent substance to another they are bent or refracted. This always happens when one of the substances is optically denser than the other, i.e. light travels less quickly in one than the other. For example, light passing from air to water is slowed down, and is bent toward the normal (a line at right-angles to the water surface). Light passing from water to air is speeded up and is bent away from the normal. The angle a light ray in water makes with the normal is always less than the angle the light ray in air makes with the normal. This there must be a certain angle at which light rays traveling in water will, after refraction, pass directly along the surface. The angle at which this happens is called the critical angle. For water the critical angle is 49°, for glass 42°, and so on. When the angle of incidence (the angle at which light rays strike the surface of separation, measured from the normal) is greater than the critical angle the light ray does not enter the second substance (e.g. air) at all; instead, it is reflected. A certain amount of reflection always takes place from a surface when refraction takes placed through it and the amount of light reflected increases with the angle of incidence until the critical angle is reached. Above this point all of the light is reflected.
Mirages and total internal reflection
Total internal reflection is easy to demonstrate with the aid of an underwater lamp. If an observer stands above the surface of the water in such a position that light rays from the lamp must strike the boundary between the water and the air at an angle greater than the critical angle in order to reach his eye, he will be unable to see the lamp. The light rays traveling in his direction will never leave the water; they will be reflected from the surface of separation between the water and the air.
Mirages are examples of total internal reflection. The conditions most likely to produce a mirage in the desert would be a layer of hot air lying immediately above the ground with cooler air above it (this is quite usual during the day because the ground becomes so hot). Light rays from a distant object, e.g. a tree, would travel in a straight line through the cool air to an observer's eye. But other light rays from the tree would travel toward the ground and come in contact with the surface of separation between the cool and the hot air with their different optical densities. The rays which struck this surface very obliquely (at an angle greater than the critical angle) would be reflected upward again and thus reach the observer's eye. In this way the observer would see the distant tree not only upright but also inverted as though mirrored in a pool of water. You can see a similar effect on heated roads during the summer. The reflection of the sky and clouds appears just above the surface of the road as though mirrored in a pool of water. This is known as an inferior mirage.
More spectacular mirages are the type sometimes seen at sea. They may take the form of a ship floating in the air, or the lights of a distant city shining in the sky. The conditions needed to produce this kind of mirage (superior mirage) are exactly opposite to those needed in the previous case. It requires a thick layer of cold air lying above the surface of the sea with warmer air above it. The light rays from the ship which travel upward and strike the surface of separation between the cold and warm air at an angle greater than the critical angle are reflected back into the eye of the distant observer. In this way an observer may see a ship mirrored in the sky, though the actual ship may be out of sight, hidden by the curve of the Earth.