The Human Eye & the Colourful World

The human eye is one of the most valuable natural optical instruments we have. It works much like a camera: it lets light in, focuses it with a lens, and forms a sharp image on a light-sensitive screen at the back of the eye.

Light passes through several parts before an image is formed. Each part has a clear job:

• Cornea: the thin, transparent front part of the eye. Most of the refraction (bending) of the light entering the eye takes place here.
• Iris: the coloured, muscular part just behind the cornea. It controls the size of the pupil.
• Pupil: the opening in the middle of the iris that lets light enter the eye. It widens in dim light and narrows in bright light to control how much light gets in.
• Eye lens (crystalline lens): a flexible convex lens made of a jelly-like material. It fine-focuses the light to form a clear image on the retina.
• Ciliary muscles: muscles that hold the eye lens and change its shape, and so change its focal length.
• Retina: the light-sensitive screen at the back of the eye. It has a large number of rod and cone cells that respond to light and generate electrical signals.
• Optic nerve: carries these signals from the retina to the brain.

The eye lens forms a real, inverted and diminished image of the object on the retina. The retina's cells send this information along the optic nerve to the brain, and the brain interprets the image as upright, so we see the world the right way up.

The ciliary muscles let the eye lens change its focal length. To see nearby objects the muscles contract and the lens becomes thicker (more curved), shortening its focal length; to see distant objects the muscles relax and the lens becomes thinner. This ability of the eye to adjust the focal length of its lens is called the power of accommodation.

A normal eye can focus objects over a wide range of distances. The closest point at which the eye can see an object clearly and comfortably, without strain, is the near point, also called the least distance of distinct vision; for a normal young adult it is about 25 cm. The farthest point the eye can see clearly is the far point, which for a normal eye is at infinity.

Look at a book in your hand, then at a distant wall. Each one looks sharp, one after the other. Yet the distance from the eye lens to the retina never changes. So how does the eye keep the image on the retina for both near and far objects? It quietly changes the focal length of its lens. This ability of the eye lens to adjust its focal length is called the power of accommodation.

The adjusting is done by the ciliary muscles, which hold the eye lens in place and can change its shape.

• To see a near object, the ciliary muscles contract. This makes the eye lens thicker and more curved, so its focal length decreases and its power increases.
• To see a distant object, the ciliary muscles relax. The lens becomes thinner and flatter, so its focal length increases.

But there is a limit to how much the lens can bulge. The closest point the eye can focus on clearly, using its full power of accommodation, is called the near point, or the least distance of distinct vision. For a normal eye it is 25 cm. The farthest point the eye can see clearly is the far point, which for a normal eye is infinity. So a normal eye can focus on everything from 25 cm right up to infinity.

If you bring an object nearer than the near point, it looks blurred. The lens simply cannot become short enough (its focal length cannot decrease any further) to bring such a close object to focus on the retina. That is why a book held too close to your eyes cannot be read comfortably.

Myopia is also called short-sightedness or near-sightedness. A person with myopia can see nearby objects clearly but cannot see distant objects clearly. In this defect, the far point of the eye is no longer at infinity — it comes closer to the eye. So a myopic person may be able to read a book comfortably, yet the writing on a distant board looks blurred.

The reason is that the image of a distant object is formed in front of the retina instead of on it. This happens because of either of these two causes:

• the eye lens has too much converging power (its focal length has become too short, due to excessive curvature of the lens), or
• the eyeball has become too long (elongated), so the retina is farther back than it should be.

To correct myopia, we use a concave (diverging) lens of suitable power. The concave lens diverges the rays coming from a distant object slightly before they enter the eye, so that the final image now falls exactly on the retina. The focal length of this correcting concave lens is equal to the distance of the defective far point from the eye — this is chosen so that an object at infinity appears to come from the far point, which the eye can already see.

Worked example. Suppose a myopic person's far point is 80 cm. The concave lens must have its focal length equal to this far point distance. Following the New Cartesian sign convention, a concave lens has a negative focal length:

1. f = −80 cm = −0.8 m
2. P = 1 / f = 1 / (−0.8 m) = −1.25 D

The power is negative, which correctly tells us the lens is concave (diverging). So this person needs spectacles of power −1.25 D.

Hypermetropia, also called far-sightedness or long-sightedness, is a defect of vision in which a person can see distant objects clearly but cannot see nearby objects clearly. For such an eye the near point has moved farther away than the normal 25 cm, so close objects appear blurred.

The reason is that the image of a nearby object is formed behind the retina instead of on it. This happens due to either of the following:

• The converging power of the eye lens is too small (its focal length is too long), so the rays are not bent enough to meet on the retina.
• The eyeball has become too short, so the retina is closer to the lens than it should be.

This defect is corrected by using a convex (converging) lens of suitable power. The convex lens provides the extra convergence that the eye is missing, bending the rays a little more so that the image of a nearby object falls exactly on the retina. Because a converging lens is used, its focal length and power are positive (P > 0).

Worked numerical: A person suffering from hypermetropia has a near point of 1 m. Find the power of the lens needed to read comfortably at the normal near point of 25 cm.

1. The correcting lens must take an object placed at 25 cm and form its virtual image at the person's near point, 1 m (100 cm), on the same side.
2. Using the New Cartesian sign convention: u = −25 cm and v = −100 cm.
3. Lens formula: 1/v − 1/u = 1/f gives 1/(−100) − 1/(−25) = 1/f, so 1/f = −1/100 + 4/100 = 3/100 per cm.
4. Therefore f = +100/3 cm ≈ +0.33 m, and P = 1/f = 1/0.33 = +3 D.

The power comes out positive, confirming that a convex lens of power +3 D is required. A positive power always tells you the correcting lens is convex, which is the giveaway for hypermetropia.

Presbyopia is a defect of vision that usually comes with old age. In this defect, the power of accommodation of the eye decreases. This happens because the ciliary muscles gradually weaken and the eye lens becomes less flexible (stiffer). As a result, the lens can no longer curve enough to focus on close objects.

Because of this, the near point of the eye recedes (moves further away). The person then finds it hard to see nearby objects clearly and comfortably — for example, reading a book or newspaper becomes difficult. In many people, presbyopia appears along with both myopia and hypermetropia at the same time, so they cannot see distant objects and nearby objects clearly.

When a person has both defects together, a single simple lens will not work. Such an eye is corrected using a bifocal lens, which has two different parts:

• The upper part is a concave lens — it corrects the myopia and is used for distant vision.
• The lower part is a convex lens — it corrects the hypermetropia and is used for near vision (such as reading).

Not every defect can be fixed with spectacle lenses. For example, in cataract the eye lens becomes cloudy and milky, so vision becomes hazy or is even lost. A cataract cannot be cured by wearing lenses — it is treated by surgery, in which the clouded lens is replaced. Today many refractive defects can also be corrected by surgical methods.

A glass prism is a transparent block with two triangular ends and three rectangular sides. Its two slanting faces (the refracting surfaces) meet at the top, and the angle between them is called the angle of the prism (A). When a ray of light passes through a prism it refracts twice — once while entering the glass and once while leaving it — and at both surfaces the ray bends towards the base. Because the two faces are not parallel (unlike a glass slab), the emergent ray does not stay parallel to the incident ray. The angle between the direction of the incident ray and the emergent ray is called the angle of deviation.

Dispersion is the splitting of white light into its seven component colours. When a narrow beam of sunlight passes through a prism, a band of colours appears on a screen. This band is called the spectrum, and its colours always appear in the fixed order VIBGYOR:

• V — Violet (bends the most)
• I — Indigo
• B — Blue
• G — Green
• Y — Yellow
• O — Orange
• R — Red (bends the least)

Dispersion happens because the different colours travel at different speeds inside the glass, so each colour bends by a different amount. Violet has the shortest wavelength and bends the most, while red has the longest wavelength and bends the least. So white light is not a single colour — it is a mixture of all seven.

Isaac Newton proved this. He first split sunlight into a spectrum using one prism. Then he placed a second, identical prism upside down (inverted) in the path of the spectrum, and the seven colours recombined to give back white light. This showed that white light is made up of these colours and can be split apart and joined together again.

A rainbow is a natural spectrum seen in the sky after rain. Tiny water droplets floating in the air act like little prisms. Sunlight entering a droplet is first refracted and dispersed, then internally reflected at the back of the droplet, and finally refracted again as it leaves. Together these steps spread the sunlight into the colours of the rainbow, which is always seen in the part of the sky opposite to the Sun.

The earth's atmosphere is not uniform. The air near the ground is denser and the air higher up is rarer, so the refractive index of air decreases with height. When light travels through these layers of gradually changing density, it bends by small amounts. This bending of light by the earth's atmosphere is called atmospheric refraction. Because the air is always moving and its temperature and density keep changing, the amount of bending also keeps changing from moment to moment.

Twinkling of stars. A star is extremely far away, so it acts as a point source of light. As starlight enters the atmosphere it is refracted continuously while passing through layers of different refractive index, bending towards the normal as it moves into denser air. Because the atmosphere keeps changing, the star's apparent position shifts slightly and the amount of light reaching our eye also keeps changing — the star looks a little brighter at one instant and fainter at the next. This flickering in position and brightness is the twinkling of stars.

Why planets do not twinkle. Planets are much closer to the earth, so they appear as an extended source — a collection of a large number of point-sized sources. The brightening and dimming from all these points do not happen together, so their variations average out. The total light reaching our eye stays almost steady, and hence planets do not twinkle.

Advance sunrise and delayed sunset. Near the horizon, sunlight passes through a thick, dense layer of atmosphere and bends, so the Sun appears raised higher than its true position. Because of this, we see the Sun about 2 minutes before it actually rises above the horizon, and for about 2 minutes after it has actually set. So atmospheric refraction makes our day appear a little longer than it really is.

The oval Sun. At sunrise and sunset the Sun often looks oval or flattened rather than perfectly round. This too is due to atmospheric refraction: light from the lower edge of the Sun is bent (raised) more than light from the upper edge, so the vertical size of the disc appears squeezed and the Sun looks flattened.

In short, atmospheric refraction explains three everyday effects:

• Twinkling of stars — starlight bends by tiny, changing amounts, so the star's position and brightness flicker; planets, being nearer and extended, do not twinkle.
• Advance sunrise and delayed sunset — we see the Sun about 2 minutes before it actually rises and about 2 minutes after it actually sets.
• Oval Sun — the Sun's disc looks flattened at sunrise and sunset.

When light travels through a medium containing tiny particles, some of it is turned aside and spread in different directions. This spreading of light by particles in its path is called scattering of light. A very important point is that the colour of the scattered light depends on the size of the particles.

The Tyndall effect is the scattering of light by very small (colloidal) particles suspended in a medium. You can see it when a fine beam of sunlight enters a dusty room, or when light passes through smoke, fog or mist. The path of the beam becomes visible because these particles scatter the light towards your eyes.

How size decides the colour:

• Very fine particles, such as the molecules of air, scatter mainly blue light, that is, light of shorter wavelength.
• Larger particles scatter light of longer wavelengths, and big enough particles can scatter all colours so that the light looks white.

This single idea explains many everyday sights:

• The clear sky is blue: the molecules of air scatter the shorter-wavelength blue light much more strongly than red. This scattered blue light reaches our eyes from all directions, so the sky looks blue.
• The sky looks dark to an astronaut: out in space there is no atmosphere to scatter sunlight, so no scattered light reaches the eyes and the sky appears dark or black even though the Sun is shining brightly.
• The Sun looks red at sunrise and sunset: near the horizon the Sun's light has to travel a much longer distance through the atmosphere. Most of the blue and shorter wavelengths are scattered away along the path, so mainly red light reaches us and the Sun appears red. At noon the Sun is nearly overhead, its light travels a shorter path, very little is scattered, and the Sun looks almost white.
• Danger signals and 'stop' lights are red: red has the longest wavelength and is scattered the least, so it travels the farthest and can be seen clearly from a distance, even through fog or smoke.