The Human Eye and the Colourful World

The eye is a roughly spherical ball about 2.3 cm in diameter, and it works like a camera: a lens system forms a real, inverted image on a light-sensitive screen at the back. Learn each part with its job, because the examiner often asks for the function of three or four parts in one question.

• Cornea: the thin transparent bulge at the front. Most of the refraction of light entering the eye happens at its outer surface, not at the eye lens. This surprises students, and it has been asked as a 1-mark item.
• Iris: the dark muscular diaphragm behind the cornea. It controls the size of the pupil.
• Pupil: the opening in the centre of the iris. It regulates and controls the amount of light entering the eye: it becomes small in bright light and large in dim light. This is why you see poorly for a while when you walk from sunlight into a dark room; the pupil takes time to open out.
• Eye lens: a fibrous, jelly-like, transparent convex lens. It provides the finer adjustment of focal length needed to focus objects at different distances on the retina.
• Ciliary muscles: hold the lens and change its curvature, and hence its focal length.
• Retina: the delicate membrane at the back with an enormous number of light-sensitive cells (rods for dim light, cones for colour and bright light). On illumination these cells generate electrical signals.
• Optic nerve: carries those signals to the brain, which interprets them so that we see the object erect even though the image on the retina is inverted.

The image formed on the retina is real, inverted and diminished. The distance between the lens and the retina is fixed, so the eye can only bring objects at different distances into focus by changing the focal length of the lens. That is the subject of the next section.

Two eyes give a wider field of view (about 180° with both, about 150° with one) and let us judge distance, since each eye sees a slightly different picture. In the box on eye donation NCERT notes that the cornea can be donated within 4 to 6 hours of death, that one pair of eyes gives sight to two corneal-blind people, and that donors with AIDS, hepatitis B or C, rabies, acute leukaemia, tetanus, cholera, meningitis or encephalitis are not accepted. A case-based passage on an eye-donation camp is a favourite.

A camera focuses by moving its lens. The eye cannot move its lens, so it changes the lens's shape instead. The ability of the eye lens to adjust its focal length is called accommodation, and the range over which it can do so is the eye's power of accommodation.

The mechanism is what the marking scheme wants, so state it in this order:

1. When the ciliary muscles are relaxed, the lens becomes thin, its focal length increases, and we see distant objects clearly.
2. When we look at a nearby object, the ciliary muscles contract, the curvature of the lens increases, the lens becomes thicker and its focal length decreases, so the image again falls on the retina.

The image distance in the eye therefore stays constant (the lens-to-retina distance) whatever the object distance; only the focal length changes. When you increase the distance of an object from the eye, the image distance does not change; the focal length of the lens increases so that the image still forms on the retina. This exact question appears in the NCERT exercise and has been asked in the board.

There is a limit to how much the lens can be squeezed. The minimum distance at which an object can be seen most distinctly without strain is the least distance of distinct vision, also called the near point. For a young adult with normal vision it is about 25 cm. Closer than that, the ciliary muscles cannot make the lens curved enough (its focal length cannot be reduced further), so the image forms behind the retina and looks blurred; this also strains the eye. The farthest point up to which the eye can see clearly is the far point, which for the normal eye is infinity. So a normal eye sees clearly from 25 cm to infinity.

Sometimes, usually in old age, the crystalline lens becomes milky and cloudy. This is a cataract; it causes partial or complete loss of vision and is corrected by cataract surgery (the lens is replaced). Do not confuse cataract with presbyopia, which is a weakening of the muscles and lens flexibility, not a clouding.

When the eye loses its power of accommodation, or the eyeball is the wrong length, images stop forming on the retina. Three refractive defects are on the syllabus. For each one the examiner wants four things: what the person cannot see, the position of the image, the causes, and the corrective lens with ray diagrams.

Myopia (near-sightedness). The person sees nearby objects clearly but cannot see distant objects distinctly; the far point has moved from infinity to a finite distance. The image of a distant object forms in front of the retina. Causes: (i) excessive curvature of the eye lens, which makes its focal length too short, or (ii) elongation of the eyeball. Correction: a concave (diverging) lens of suitable power. The concave lens forms the image of a distant object at the person's own far point; the eye can then focus that image onto the retina. The focal length of the lens equals the distance of the far point: f = −(far point).

Hypermetropia (far-sightedness). The person sees distant objects clearly but cannot see nearby objects distinctly; the near point has moved beyond 25 cm. Rays from a nearby object are focused behind the retina. Causes: (i) the focal length of the eye lens is too long, or (ii) the eyeball has become too small. Correction: a convex (converging) lens of suitable power. The convex lens forms a virtual image of an object placed at 25 cm at the person's near point, from where the eye can focus it. Use the lens formula with u = −25 cm and v = −(near point).

Presbyopia. With age the ciliary muscles weaken and the lens loses flexibility, so the power of accommodation falls and the near point recedes. Older people therefore find it hard to read without spectacles. Sometimes the same person has both myopia and hypermetropia; the remedy is a bifocal lens: the upper part is concave for distant vision, the lower part is convex for reading. Nowadays contact lenses and surgery are also used.

The ray diagrams earn most of the marks. For myopia draw (a) parallel rays from a distant object converging in front of the retina, (b) the eye's far point with rays from it focused on the retina, (c) a concave lens in front of the eye diverging parallel rays so that they appear to come from the far point and then focus on the retina. For hypermetropia draw (a) rays from an object at 25 cm converging behind the retina, (b) rays from the near point N focused on the retina, (c) a convex lens making rays from 25 cm appear to come from N so they focus on the retina. Label the eye, the lens, N or the far point, and the retina.

A glass prism has two triangular bases and three rectangular lateral surfaces. Unlike a rectangular glass slab, whose faces are parallel, the refracting surfaces of a prism are inclined to each other. The angle between its two lateral faces is the angle of the prism, A.

NCERT Activity 10.1 traces a ray through a prism on a sheet of paper. Fix the prism, mark its outline ABC, draw a line PE meeting face AB at E, fix pins P and Q on it, then look through the other face AC and fix pins R and S in line with the images of P and Q. Remove everything and join the marks. PE is the incident ray, EF is the refracted ray inside the prism, and FS is the emergent ray. Draw normals at E and F and mark the angle of incidence ∠i, the angle of refraction ∠r and the angle of emergence ∠e.

Two things to notice. First, at the first surface light goes from air to glass, so it bends towards the normal; at the second surface it goes from glass to air, so it bends away from the normal. Because the faces are inclined, both bends are in the same direction, and the net effect is that the ray bends towards the base of the prism. Second, the emergent ray is not parallel to the incident ray (in a glass slab it is). The angle between the direction of the incident ray produced forward and the emergent ray is the angle of deviation, ∠D. Mark it on the diagram; it is the label most often missed.

In the exam the prism diagram is asked on its own as a 2-mark item ('draw the path of a ray of light through a glass prism and mark the angle of deviation') and also as the first half of a dispersion question. Practise it until you can draw it from memory in under a minute with all six labels: i, r, e, A, D and the three rays.

When a narrow beam of white light passes through a glass prism it splits into a band of seven colours: violet, indigo, blue, green, yellow, orange, red (VIBGYOR). The band of coloured components of a light beam is called a spectrum, and the splitting of light into its component colours is called dispersion. Red appears at the top of the band (closest to the original direction) and violet at the bottom (nearest the base of the prism) when the prism stands on its base.

Why does it happen? Different colours of light bend through different angles with respect to the incident ray as they pass through the prism, because they travel at different speeds in glass. Red light bends the least and violet the most, so the colours emerge along different paths and become distinct. White light is therefore not a single colour but a mixture; the prism only separates what was already there. Say 'different colours have different speeds in glass, so they refract by different amounts'. The board answer does not need wavelengths, but it does no harm to add that violet has the shortest wavelength and red the longest.

Newton's experiment. Isaac Newton was the first to use a glass prism to obtain the spectrum of sunlight. He then tried to split the colours further with a second prism and could not. Placing a second identical prism inverted with respect to the first, so that all the colours of the spectrum pass through it, gave a beam of white light emerging from the second prism. This recombination proved that white light is composed of the seven colours and that the prism does not itself add colour. The diagram of the two prisms (one upright, one inverted, white in, spectrum between, white out) is a frequent 3-mark item.

Rainbow. A rainbow is a natural spectrum that appears in the sky after a rain shower. It is caused by dispersion of sunlight by tiny water droplets in the atmosphere. Each droplet acts as a small prism: sunlight entering the drop is refracted and dispersed, then internally reflected from the back of the drop, and finally refracted again as it comes out. The three steps together spread the colours in the sky. Two conditions are needed to see one: the Sun must be behind the observer and water droplets must be in front. In the diagram of a single drop, mark the point of dispersion, the internal reflection and the final refraction, with red on the outside and violet on the inside of the bow.

The air above us is not uniform. Its density, and so its refractive index, changes with height and with temperature, and it keeps changing from moment to moment. Light passing through it therefore does not travel in a straight line; the refraction of light by the earth's atmosphere is called atmospheric refraction. NCERT introduces it with the shimmering seen above a fire or a hot road: hot air above the fire is lighter (less dense) and has a slightly smaller refractive index than the cooler air above it, and because the hot air keeps rising, the apparent position of objects seen through it wavers. The same thing on the scale of the atmosphere explains four phenomena, and the board asks any two.

1. Twinkling of stars. Starlight, on entering the atmosphere, undergoes continuous refraction as it passes through layers of gradually changing refractive index, bending towards the normal each time it enters a denser layer. The apparent position of the star is thus slightly different from its actual position, and because the atmosphere is not stationary the apparent position keeps changing slightly and the amount of light entering the eye flickers. The star sometimes appears brighter and sometimes fainter: this is twinkling.

2. Stars appear higher than they are. Since the light bends towards the normal as it enters denser and denser air, and we see the star along the direction from which the light finally reaches us, the star appears slightly above its actual position. Draw the curved ray from the actual star, the straight line of sight to the apparent star, and the layers of atmosphere with increasing density towards the ground.

3. Planets do not twinkle. Planets are much closer to the earth, so they are seen as extended sources, a collection of a large number of point-sized sources. The variations in the light from all these points average out to zero, so there is no net twinkling. Stars are so far away that they are effectively point sources.

4. Advance sunrise and delayed sunset. The Sun is visible about two minutes before actual sunrise and about two minutes after actual sunset because of atmospheric refraction. Light from the Sun below the horizon bends as it enters the atmosphere, so the Sun appears above the horizon while it is actually below. The apparent flattening of the Sun's disc at sunrise and sunset is also due to the same effect.

When light falls on very small particles it is thrown off in all directions; this is scattering. The interplay of light with objects around us gives rise to several spectacular phenomena in nature: the blue colour of the sky, the colour of water in the deep sea, and the reddening of the Sun at sunrise and sunset.

Tyndall effect. The earth's atmosphere is a heterogeneous mixture of minute particles: smoke, tiny water droplets, suspended particles of dust and molecules of air. When a beam of light strikes such fine particles, its path becomes visible because the particles scatter the light, and the scattered light reaches us. The scattering of light by colloidal particles is the Tyndall effect. Two examples come straight from NCERT: a fine beam of sunlight entering a smoke-filled room through a small hole, and sunlight passing through the canopy of a dense forest, where tiny water droplets in the mist scatter the light. Other examples the board has accepted: fog or mist lit by headlights, a laser beam passing through diluted milk or a colloidal solution. A true solution shows no Tyndall effect because its particles are too small to scatter light.

Colour of scattered light depends on particle size. This one sentence is worth a mark on its own. Very fine particles scatter mainly blue light (shorter wavelengths). Particles of larger size scatter light of longer wavelengths; and if the scattering particles are large enough, the scattered light may appear white. That is why clouds and fog look white: their water droplets are large compared with the wavelength of light and scatter all colours nearly equally.

How to distinguish scattering from reflection when asked: reflection happens at a smooth surface and sends light in one definite direction; scattering happens at tiny particles and sends light in all directions, which is why it makes the beam's path visible from the side.

The molecules of air and other fine particles in the atmosphere have sizes smaller than the wavelength of visible light. Such particles are more effective in scattering light of shorter wavelengths at the blue end of the spectrum than light of longer wavelengths at the red end. (Red light has a wavelength about 1.8 times that of blue light.) When sunlight passes through the atmosphere, the fine particles scatter blue light much more strongly than red. This scattered blue light enters our eyes from every direction of the sky, so the clear sky looks blue.

The same idea answers a cluster of standard questions:

• Why is 'danger' signalled with red? Red is scattered the least by fog or smoke because it has the longest wavelength, so a red signal is visible from far away and in poor weather.
• Why does the sky look dark to an astronaut, or from a very high altitude, or on the Moon? There is no, or hardly any, atmosphere and hence no particles to scatter sunlight. With no scattered light reaching the eye, the sky appears dark (black) instead of blue.
• Why is the sky blue but the Sun white or yellow? Most of the direct sunlight still reaches us unscattered; only the blue component is spread across the sky.

The rationalised NCERT has dropped the separate sub-section on the reddish Sun at sunrise and sunset, but the explanation is one line and older papers ask it, so keep it: near the horizon sunlight travels through a much thicker layer of air, most of the blue is scattered away before the light reaches us, and the light that survives is rich in red, so the Sun and the sky near it look reddish. At noon the path is shortest and the Sun looks nearly white.

In an Assertion-Reason item watch the Reason carefully. 'The sky appears blue because blue light is scattered the most by fine particles' is correct. 'Because blue has the longest wavelength' is wrong; 'because red is scattered the most' is wrong. And the CBSE 2021 item had both statements true but the Reason (a general statement about scattering) not explaining the Assertion, so read whether the Reason actually causes the Assertion before ticking option (a).