The Human Eye and the Colourful World: Class 10 Science · Chapter 10

Read the number on a bus as it pulls away, then glance down at the ticket in your hand. Both are sharp within a moment, and you did nothing to make that happen. Your eyes did the work. In the last chapter you met lenses and the images they form. Here you will see that each eye carries its own adjustable lens, and that spectacles are simply extra lenses that help it.

The second half of the chapter looks outward. Light passing through glass, raindrops and the air itself produces some everyday wonders: a band of colours from a prism, a rainbow over a wet highway, stars that flicker, a Sun that rises a little early and a sky that is blue. Each has a reason you can explain with refraction and scattering.

10.1 The Human Eye

Imagine choosing a sari or a cricket jersey with your eyes closed. Touch tells you the cloth is soft, but nothing tells you whether it is maroon or navy blue. Colour and detail at a distance reach us only through sight, which is why the eye is one of our most precious sense organs.

Think of the eye as a living camera packed into a ball roughly 2.3 cm wide. Some parts focus the light, some control how much of it gets in, and one turns the picture into signals for the brain. Follow Fig. 10.1 as you meet each part.

Focusing is shared between two parts. The first is the cornea (स्वच्छ मंडल), the clear dome at the very front, like the glass of a watch. Light bends most sharply where it enters the cornea, so the cornea does the bulk of the focusing. The second is the crystalline eye lens, a clear, jelly-like lens a little deeper inside. It adds a small, adjustable amount of bending, just enough to sharpen near or far objects.

Two parts control the light. The iris is the coloured ring you notice in someone's eyes; it is made of muscle. The dark circle at its centre, the pupil, is simply a hole. The iris widens the pupil in dim light and narrows it in bright light, which protects the back of the eye from glare.

One part senses, one part reports. The cornea and lens together form a real, inverted image on the retina (दृष्टिपटल), the lining at the back. The retina carries millions of light-sensitive cells. Light switches them on and they fire tiny electrical signals. The optic nerve, a cable of nerve fibres, takes these signals to the brain, which reads them as the upright scene you see.

10.1.1 Power of Accommodation

A camera focuses by moving its lens closer to or farther from the sensor. Your eye cannot do that: the distance from the eye lens to the retina stays fixed. Instead, the eye changes the shape of its lens, and with it the focal length.

Rays from a nearby object arrive at the eye spreading out steeply, so they need a strong lens with a short focal length. For this the ciliary muscles (पक्ष्माभी पेशियाँ) around the lens tighten; the soft lens bulges, its curvature grows and its focal length shrinks. Rays from a distant object arrive almost parallel and need only a weak lens. Then the muscles let go, the lens is pulled flatter, and its focal length grows until the parallel rays meet exactly on the retina. Step through Fig. 10.2 to see both cases.

Accommodation has limits. The lens can only bulge so much, so its focal length has a smallest possible value. Hold a needle almost touching your nose and try to see its eye: you cannot, and your eyes soon tire. The closest distance at which you can read comfortably, without strain, is called the near point. Its other name is the least distance of distinct vision. With healthy eyes, a young adult's near point is about 25 cm.

At the other end, the far point is the farthest distance at which the eye can still see clearly. For a normal eye it is at infinity: the eye can focus on a distant hill or the Moon with its muscles fully relaxed. So a normal eye sees clearly everything from about 25 cm out to infinity.

10.2 Defects of Vision and Their Correction

Look around your classroom: several of your friends probably wear spectacles. Their eyes cannot quite bring the image onto the retina, so without help part of the world looks blurred. Usually the cause is the shape of the eyeball or the focusing power of the eye, and such problems are called refractive defects. The three most common are myopia, hypermetropia and presbyopia. Each can be corrected with spherical lenses of the right kind and power, which is what spectacles are.

Myopia (near-sightedness)

In a myopic eye the focusing is too strong for distant objects. Parallel rays from a far-off hoarding come to a focus before they reach the retina, then cross and spread, so the retina gets a blurred patch instead of a point. Rays from a nearby object arrive spreading out and are still focused well. So a person with myopia (निकट-दृष्टि दोष) reads easily but struggles with the board, road signs or a ball in the outfield. Their far point has moved in from infinity to perhaps a couple of metres, sometimes much less.

There are two usual reasons for the extra focusing. The eye lens may be more curved than it should be, or the eyeball may have grown too long from front to back, so the retina sits behind the point of focus.

The fix is a concave lens of suitable power. It spreads the parallel rays from a distant object so that they seem to come from the person's far point. The eye can already focus objects at its far point, so the image lands on the retina again. See Fig. 10.3.

Where does (10.1) come from? An object at infinity ($u=-\mathrm{\infty }$) must give a virtual image at the far point ($v=-x_F$). The lens formula then gives $1\mathrm{/}f=-1\mathrm{/}{x}_F$. We treat the spectacle lens as touching the eye, which is close enough for spectacles.

Hypermetropia (far-sightedness)

Hypermetropia (दीर्घ-दृष्टि दोष) is the opposite fault: the eye's focusing is too weak. For distant objects the eye can still manage by working its ciliary muscles, so far things look clear. But rays from a book held close spread out more steeply, and even the most curved lens cannot pull them together in time; they would meet behind the retina. The near point is pushed out well beyond 25 cm. A child with this problem may hold her book far away and get headaches after reading.

Why is the focusing weak? Either the eyeball is too short, so the retina is too close to the lens, or the eye lens has too long a focal length.

The cure is to put some converging power in front of the eye: a convex lens. It bends the rays from a book at 25 cm so that they seem to come from the person's own near point, where the eye can cope. Compare the three steps of Fig. 10.4.

(10.2) comes from the lens formula with the book at $u=-d$ and its virtual image at $v=-x_N$. Because $x_N$ is larger than $d$, the focal length comes out positive: a convex lens.

Presbyopia

As people grow older, the ciliary muscles weaken and the eye lens stiffens. The power of accommodation falls, and the near point slowly moves away. Many people over forty notice that they must hold their phone farther away to read it. This age-related defect is called presbyopia (जरा-दूरदृष्टिता). Reading glasses with convex lenses help.

Some people need help both ways: distant objects blur and close print blurs. Their spectacles are made in two zones, a concave zone at the top for distance and a convex zone at the bottom for reading. Such lenses are called bifocals. The wearer simply looks up or down through the right zone, as in Fig. 10.5.

Today refractive defects can also be corrected with contact lenses, which sit directly on the cornea, or with laser surgery that reshapes the cornea. An eye doctor checks which option suits each person.

10.3 Refraction of Light through a Prism

Look at a door frame through a glass prism held near your eye. The frame seems to have jumped to one side, so the prism must be turning the light that passes through it. A rectangular glass slab does not do this. Its two faces are parallel, so the bend at the second face undoes the bend at the first, and the ray only shifts sideways.

A triangular prism is different. It has two triangular ends and three rectangular side faces. Light passes in through one side face and out through another, and these two faces lean towards each other. The angle between them is the angle of the prism; it is 60° for the common equilateral prism. Trace a ray through one in the activity below.

Fig. 10.7 shows the path step by step. The ray bends twice, both times towards the base, so the bends add up instead of cancelling. The angle between the direction of the incident ray and the direction of the emergent ray is the angle of deviation (विचलन कोण), $D$. Measure it in your activity.

10.4 Dispersion of White Light by a Glass Prism

Sunlight falling on the cut-glass edge of a mirror or a chandelier sometimes throws little patches of colour on the wall. Yet sunlight itself looks colourless. Where do the colours come from? A prism lets us find out.

What you see is a spectrum (स्पेक्ट्रम): white light opened out into a band of colours. Seven names are traditionally given to them, violet, indigo and blue at one end, green and yellow in the middle, orange and red at the other. Their initials, VIBGYOR, help you remember the order. The colours actually blend smoothly, so do not worry if you cannot find a sharp edge between indigo and blue. This opening-out of white light into colours is called dispersion (विक्षेपण).

The reason lies in the glass. Violet light travels through glass a little more slowly than red light, so glass has a slightly higher refractive index for violet. Violet is therefore turned through the largest angle and red through the smallest, with the other colours in between. By the time the light reaches the screen, the colours have fanned out side by side, as Fig. 10.8 shows.

Newton's two prisms

Are the colours made by the prism, or were they in the sunlight all along? Newton's answer came from two more tests. In one, he blocked all of the spectrum except a single colour and sent that colour through a second prism. It was bent again but stayed exactly the same colour: a prism cannot create new colours. In the other, he turned a second, matching prism upside down and set it close to the first. The second prism undid the spreading, the colours merged, and a white beam came out. Step through Fig. 10.9.

So sunlight is a mixture of colours, and the prism only sorts them out. Light from a hot filament or a white LED that opens out into the same full band of colours is also called white light.

The rainbow

After a monsoon shower, if the Sun breaks through behind you while rain is still falling ahead, you may see a rainbow: a spectrum stretched across the sky by millions of raindrops. It is always on the side of the sky opposite the Sun, never towards it.

Follow one ray of sunlight into a drop in Fig. 10.10. As it enters the curved surface it is refracted, and because water, like glass, bends violet more than red, it begins to split. It crosses the drop and meets the back surface, where it is reflected inside the drop. It is refracted once more as it leaves, which spreads the colours further apart. The light leaves heading back towards the Sun's side, which is why the Sun must be behind you. Each drop sends red out at a slightly steeper angle than violet, so red reaches you from higher drops and violet from lower ones.

10.5 Atmospheric Refraction

Look across the top of a hot tandoor, or along a highway on a May afternoon, and things on the far side seem to shiver. Hot air is thinner than cool air, and thinner air bends light a little less: its refractive index is slightly lower. Above the tandoor, pockets of hot and cooler air keep rising and swirling past each other, so the bending keeps changing. Whatever you see through them seems to quiver.

Bending of light by air whose refractive index varies is called atmospheric refraction (वायुमंडलीय अपवर्तन). Above the tandoor it happens over a metre or so. For starlight and sunlight it happens over the hundreds of kilometres of air above us.

Twinkling of stars

Air is densest near the ground and gets thinner with height, so its refractive index decreases gradually upwards. Starlight entering the atmosphere therefore travels from thinner into denser air all the way down. It keeps bending towards the normal, so its path curves gently, as in Fig. 10.11.

Your eye sees the star in the direction from which the light finally arrives. That direction is steeper than the true one, so a star appears slightly higher than it really is. The effect is largest for stars near the horizon.

Now add wind. Warm and cool cells of air drift across the line of sight all the time, like the swirls above the tandoor, and each one nudges the starlight slightly. A star is so distant that its light reaches us as an extremely fine pencil of rays from a single point. One nudge can steer much of that pencil away from your pupil, and the next can steer it back. So the star's brightness flickers many times a second and its position jitters a little. That flicker is twinkling.

A planet is a different story. It is so much nearer that its light comes from a tiny disc, an extended source, even though it looks like a point to the eye (a telescope shows the disc clearly). Light from one edge of the disc and from the other passes through slightly different air. While one part of the disc is dimmed, another is brightened, and the total reaching your eye hardly changes. So Venus, Jupiter and Mars shine with a steady light.

Advance sunrise and delayed sunset

Astronomers time sunrise as the moment the Sun's disc truly crosses the horizon. You see it a little sooner. While the Sun is still just below the horizon, its light curves as it passes into denser and denser air, bends over the curve of the Earth and reaches your eye. You see the Sun in the direction from which that light arrives, which is just above the horizon.

The gain is about 2 minutes in the morning, and the evening works the same way in reverse: the Sun stays in view for about 2 minutes after it has really set. Together, these add a few minutes of daylight every day. The same effect makes the Sun's disc look slightly flattened near the horizon. Light from its lower edge passes through more air and is lifted more than light from the upper edge. See Fig. 10.12.

10.6 Scattering of Light

Remember shining a torch through salt water and through milky water in Class 9? In the salt solution the beam was invisible from the side; in the colloid, whose particles are much bigger, it showed up as a glowing path. That simple observation is the key to some of nature's most beautiful colours: the blue of the clear sky, the blue of deep sea water and the red Sun at dawn and dusk.

10.6.1 Tyndall Effect

When light meets a very small particle, the particle sends some of that light off in all directions. This is scattering (प्रकीर्णन). The air around us is full of scatterers: its own molecules, plus specks of dust and smoke and tiny water droplets. Some of the light scattered by the particles in a beam heads sideways, into your eyes, so you can see where the beam runs.

The scattering of light by particles, which makes the path of a beam visible, is the Tyndall effect (टिंडल प्रभाव). You see it in the beam of a cinema projector, in car headlights on a foggy winter night, and in a torch beam in a dusty room, as in Fig. 10.13.

Particle size matters. The tinier the particle, the more it favours blue, the short-wavelength end of the spectrum. Bigger particles scatter the longer wavelengths too, and particles as big as cloud droplets scatter every colour about equally, so their scattered light is white. That is why clouds look white while the clear sky around them is blue.

10.6.2 Why is the Colour of the Clear Sky Blue?

Look at the sky away from the Sun: it glows, even though the Sun is not there. That glow is sunlight scattered towards you by the air itself. Air molecules are far smaller than the wavelength of light, and scatterers that small are choosy. They scatter short wavelengths much more than long ones, so blue, whose wavelength is a little over half that of red, is scattered far more strongly.11Red light's wavelength is about 1.8 times that of blue. For scatterers much smaller than the wavelength, this makes blue scattered roughly ten times more strongly than red.

So as sunlight crosses the atmosphere, its blue part is sprayed across the whole sky, while most of the red, orange and yellow carries straight on. Wherever you look, away from the Sun, the light reaching you is mostly this scattered blue. Follow Fig. 10.14.

Take the air away and the blue goes with it. The Moon has no air, and photographs taken there show the Sun blazing in a black sky. Even from a jet flying very high, the sky overhead looks a deeper, darker blue, because much of the air is now below you.

Scattering also explains why danger signals are red. Red light is scattered the least by fog, smoke and dust. A red tail-light, a red light on top of a mobile tower or a red railway signal therefore stays bright and red even at a distance in haze, when other colours would fade.