The Human Eye and the Colourful World

The eyeball is roughly spherical and about 2.3 cm across. Light enters through a thin membrane, the cornea. Most of the bending happens at the outer surface of the cornea. The crystalline lens only makes the fine adjustment of focal length.

Behind the cornea is the iris. This dark muscular diaphragm changes the size of the pupil and so controls how much light enters. The lens forms an inverted, real image on the retina. Light-sensitive cells of the retina make electrical signals. The signals travel to the brain along the optic nerve.

The lens is a fibrous, jelly-like material. The ciliary muscles can change its curvature a little. When the muscles are relaxed the lens becomes thin, the focal length increases and a distant object is clear. For a nearby object the muscles contract, the lens thickens and the focal length decreases.

The focal length cannot be made shorter than a limit. The smallest distance for clear, comfortable vision is the least distance of distinct vision. It is also called the near point. For a young adult with normal vision it is about 25 cm. The far point is infinity. A page held closer than this looks blurred and the eye feels strained.

In myopia nearby objects are clear and distant ones are not. The far point comes closer than infinity. The image of a distant object forms in front of the retina. Two causes are possible — the lens is too curved, or the eyeball has become too long. A concave lens of suitable power corrects it.

In hypermetropia distant objects are clear and nearby ones are not. The near point shifts farther than 25 cm. The image of a nearby object forms behind the retina. The cause is a focal length that is too long, or an eyeball that is too small. A convex lens of suitable power corrects it.

For most people the near point slowly recedes with age. Nearby objects are no longer comfortable without glasses. This defect is presbyopia. The ciliary muscles gradually weaken and the lens loses flexibility.

Sometimes one person has both myopia and hypermetropia. Then a bifocal lens is used. The upper part is concave, for distant vision. The lower part is convex, for reading. These defects can also be corrected with contact lenses or by surgery.

In old age the lens sometimes becomes milky and cloudy. This is cataract. Vision may be lost in part or fully. Surgery can restore it.

The two faces of a glass slab are parallel, so the emergent ray stays parallel to the incident ray and only shifts sideways. The refracting faces of a prism are inclined to each other. The angle between the two lateral faces is the angle of the prism (∠A).

Because of the shape of the prism, the emergent ray bends at an angle to the direction of the incident ray. That angle is the angle of deviation (∠D).

Each colour bends through a different angle from the incident ray. Red bends the least and violet bends the most. So each colour leaves along its own path and stands apart on the screen.

Newton first obtained the spectrum of sunlight with a glass prism. A second prism used the same way did not split the colours any further. When a second identical prism was placed inverted relative to the first, all the colours passed through it and white light came out on the other side. Light that gives a spectrum like sunlight is called white light.

A rainbow forms in the sky after rain, in the direction opposite the sun. Tiny water drops act as prisms. They refract and disperse the sunlight, then reflect it inside the drop, and refract it again as it comes out. With the sun behind you, a rainbow can also be seen in a waterfall or a fountain.

The hot air above a fire is lighter than the cooler air and has a slightly smaller refractive index. The medium does not stay still, so the apparent position of an object keeps wavering. That is atmospheric refraction on a small scale.

Starlight bends continuously in the atmosphere. Near the horizon a star appears slightly higher than its real position. The state of the atmosphere keeps changing, so the apparent position changes too. Stars are so far away that they behave as point sources. The light entering the eye is sometimes more and sometimes less — that is the twinkling.

Planets do not twinkle. They are nearer the earth and look like extended sources. The variations from a large number of point sources average out to zero.

The path of a beam through a true solution is not visible. In a colloidal solution the particles are larger, so the path of the beam becomes visible. Scattering of light by those particles produces this effect. It is called the Tyndall effect.

The atmosphere is a mixture of smoke, tiny water droplets, dust and molecules of air. A sunbeam entering a smoke-filled room through a small hole, or sunlight filtering through the mist of a dense forest, are examples. Very fine particles scatter mainly blue light. Larger particles scatter longer wavelengths. If the particles are large enough, the scattered light can even look white.

Molecules of air and other fine particles are smaller than the wavelength of visible light. They scatter the shorter waves at the blue end more than the longer waves at the red end. The wavelength of red light is about 1.8 times that of blue light. The scattered blue light enters our eyes, so the clear sky looks blue.

With no atmosphere there would be no scattering and the sky would look dark. Passengers flying very high see a dark sky. At sunrise and sunset the light travels a long path through the atmosphere. Blue is scattered away on the way, and the less-scattered red light reaches the eye. Danger signals are red for the same reason — fog or smoke scatters red the least, so the colour stays the same at a distance.