The Human Eye and the Colourful World

1. The human eye — structure

The eye is our most valuable sense organ — it alone lets us see colour. It behaves like a tiny camera: its lens system forms an image on a light-sensitive screen, the retina. The eyeball is roughly spherical, about 2.3 cm in diameter. Tracing a ray of light from outside in:

• Cornea — the transparent bulge at the front. Light enters here, and most of the bending (refraction) happens at the cornea's outer surface, not the lens.
• Aqueous humour — the watery fluid just behind the cornea.
• Iris — the coloured muscular diaphragm behind the cornea; it controls the size of the pupil.
• Pupil — the central opening; it regulates the amount of light entering the eye (small in bright light, wide in dim light).
• Crystalline lens (eye-lens) — a flexible, jelly-like convex lens. It does the fine adjustment of focal length to focus objects at different distances.
• Ciliary muscles — hold the lens and change its curvature (and hence its focal length).
• Retina — the light-sensitive screen at the back, packed with cells that turn light into electrical signals.
• Optic nerve — carries those signals to the brain, which finally interprets them so we "see".
• Vitreous humour — the jelly filling the main chamber of the eyeball.

The image formed on the retina is real and inverted — the brain flips it so we perceive objects upright.

2. Power of accommodation

The eye-lens is made of a fibrous, jelly-like material whose curvature the ciliary muscles can change:

• Distant object: ciliary muscles relax → lens becomes thin → focal length increases → distant objects are seen clearly.
• Nearby object: ciliary muscles contract → lens becomes thick → focal length decreases → nearby objects are seen clearly.

This ability of the eye-lens to adjust its focal length is called accommodation. But the focal length cannot be reduced below a minimum limit — so very close objects look blurred and strain the eye.

• Near point (least distance of distinct vision): the closest distance at which the eye can see clearly without strain. For a young adult with normal vision it is about 25 cm.
• Far point: the farthest distance up to which the eye can see clearly — infinity for a normal eye.

So a normal eye sees clearly everything between 25 cm and infinity. Cataract: in old age the crystalline lens may become milky and cloudy, causing partial or complete loss of vision; it is restored by cataract surgery.

3. Refraction reminder & the lens-power formulae

The numericals in this chapter use formulae you met in the previous chapter. Keep these handy:

Sign convention (distances measured from the optical centre, in the direction of incident light positive): a convex (converging) lens has $f>0$ so power $P>0$; a concave (diverging) lens has $f<0$ so power $P<0$. Power is large when $f$ is small.

4. Defect 1 — Myopia (near-sightedness)

A myopic person can see nearby objects clearly but not distant objects. The far point comes closer than infinity — they may see clearly only up to a few metres.

Why: the image of a distant object forms in front of the retina, not on it. This happens because of (i) excessive curvature of the eye-lens, or (ii) elongation of the eyeball.

Correction: use a concave (diverging) lens of suitable power. It diverges the parallel rays from a distant object just enough so that the eye-lens then forms the image on the retina. The lens must form a virtual image of a very distant object at the eye's far point.

5. Defect 2 — Hypermetropia (far-sightedness)

A hypermetropic person can see distant objects clearly but not nearby objects. The near point recedes farther than the normal 25 cm, so reading material must be held well beyond 25 cm.

Why: light from a nearby object is focussed at a point behind the retina. This happens because (i) the focal length of the eye-lens is too long, or (ii) the eyeball has become too small.

Correction: use a convex (converging) lens of suitable power. It provides the extra converging power so a nearby object at 25 cm appears to come from the eye's actual (farther) near point.

6. Defect 3 — Presbyopia, and bi-focal lenses

Presbyopia appears with ageing: the power of accommodation decreases, the near point gradually recedes, and nearby objects cannot be seen comfortably without glasses. It arises from weakening of the ciliary muscles and decreasing flexibility of the eye-lens.

Sometimes a person has both myopia and hypermetropia. Then a bi-focal lens is used: its upper part is a concave lens (for distant vision) and its lower part is a convex lens (for near/reading vision). These days, defects can also be corrected with contact lenses or by surgery.

7. Refraction of light through a prism

A triangular glass prism has two triangular bases and three rectangular faces. The angle between its two refracting (lateral) faces is the angle of the prism ($\angle A$).

Trace a ray PE striking face AB. At AB the ray goes from air to glass, so it bends towards the normal. Inside the glass it travels as EF. At face AC it goes from glass to air, so it bends away from the normal and emerges as FS.

Unlike a glass slab (where the emergent ray is parallel to the incident ray), the prism's inclined faces make the emergent ray bend at an angle to the original direction. This angle is the angle of deviation ($\angle D$). Net effect: the prism bends the light towards its base. The relevant angles are $\angle i$ (incidence), $\angle r$ (refraction), $\angle e$ (emergence) and $\angle D$ (deviation).

8. Dispersion of white light by a prism

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 — remember it as VIBGYOR. This band is the spectrum, and the splitting of light into its components is called dispersion.

Why colours separate: different colours bend through different angles on passing through the prism. Red bends the least and violet bends the most, so each colour travels a slightly different path and becomes distinct.

9. Atmospheric refraction

The air in the atmosphere is not uniform — its density (and so its refractive index) varies with temperature and height. Light passing through this changing medium keeps bending slightly. A familiar small-scale example: objects seen through the hot, shimmering air above a fire or radiator appear to waver, because the hot air just above the flame is lighter (less dense) than the cooler air above, and these conditions keep fluctuating.

Twinkling of stars. Starlight entering the earth's atmosphere is refracted continuously before reaching us. Because the atmosphere bends starlight towards the normal, a star's apparent position is slightly higher than its actual position (most noticeable near the horizon). Stars are so distant they act as point sources; as the air's conditions keep changing, the path of starlight varies, so the amount of starlight entering the eye keeps fluctuating — the star looks brighter at one moment and fainter the next. This flickering is the twinkling of stars.

Why planets do not twinkle. Planets are much closer, so they appear as extended sources — effectively a large collection of point sources. The variations in light from all these points average out to zero, so the total light entering the eye stays steady and the planet does not twinkle.

Advance sunrise and delayed sunset. The Sun is visible to us about 2 minutes before the actual sunrise and about 2 minutes after the actual sunset — because atmospheric refraction bends the sunlight so we can see the Sun even when it is just below the horizon. ("Actual" sunrise/sunset means the real crossing of the horizon.) The same refraction also makes the Sun's disc appear flattened (oval) at sunrise and sunset.

10. Scattering of light

When light interacts with tiny particles, it is scattered in different directions. This explains the blue sky, the deep-sea blue, and the red Sun at sunrise/sunset.

Tyndall effect. The atmosphere is a mixture of minute particles — smoke, tiny water droplets, dust, air molecules. When a beam of light strikes such fine particles, its path becomes visible because light is reflected/scattered diffusely by them. This scattering of light by colloidal particles is the Tyndall effect — seen when a fine beam of sunlight enters a smoke-filled room through a small hole, or sunlight passes through the mist in a dense forest. The colour of scattered light depends on the size of the particles: very fine particles scatter mainly blue light, while larger particles scatter longer wavelengths; very large particles can scatter all wavelengths so the scattered light looks white.

Why the clear sky is blue. The molecules of air and other fine particles are smaller than the wavelength of visible light. Such particles scatter shorter wavelengths (blue) much more effectively than the longer wavelengths (red) — red light has a wavelength about 1.8 times that of blue. So as sunlight passes through the atmosphere, blue is scattered more strongly and reaches our eyes from all directions, making the sky look blue. If the earth had no atmosphere there would be no scattering, and the sky would look dark — which is why the sky looks dark to astronauts and to passengers at very high altitudes.

Why the Sun looks red at sunrise/sunset. Near the horizon, sunlight travels through a much greater thickness of atmosphere than at noon. Most of the blue (shorter wavelengths) is scattered out of the line of sight along the way, so mainly the longer-wavelength red light reaches us — the Sun appears red. At noon the Sun is overhead, light travels through less air, relatively little is scattered, so the Sun appears nearly white. 'Danger' signals are red because red is least scattered by fog or smoke and so is seen clearly from far away.

11. NCERT in-text Questions — fully answered

Q1. What is meant by power of accommodation of the eye?
It is the ability of the eye-lens to adjust its focal length (by the ciliary muscles changing its curvature) so the eye can clearly focus objects at different distances, from the near point (25 cm) to infinity.

Q2. A person with a myopic eye cannot see objects beyond 1.2 m distinctly. What should be the type of the corrective lens?
This is myopia, so a concave (diverging) lens is needed. Its focal length must make a very distant object appear at the far point, 1.2 m: $f=-1.2\text{ m}$. Power $P=\dfrac{1}{f}=\dfrac{1}{-1.2}=-0.83\text{ D}$ — a concave lens of about $-0.83$ D.

Q3. What is the far point and near point of the human eye with normal vision?
Near point = 25 cm (least distance of distinct vision); far point = infinity.

Q4. A student has difficulty reading the blackboard while sitting in the last row. What defect is this and how is it corrected?
The student cannot see distant objects clearly → myopia (near-sightedness). Corrected with a concave lens of suitable power.

12. NCERT Exercises 1–4 (MCQ-type) — answered

Q1. Focusing on objects at different distances by adjusting focal length is due to → (b) accommodation.

Q2. The eye forms the image of an object at its → (d) retina.

Q3. The least distance of distinct vision for a young adult is about → (c) 25 cm.

Q4. The change in focal length of the eye-lens is caused by the action of the → (c) ciliary muscles.

13. NCERT Exercise Q5 — distant & near vision powers

14. NCERT Exercise Q6 — myopic far point 80 cm

15. NCERT Exercise Q7 — hypermetropic near point 1 m

16. NCERT Exercises 8–12 — answered

Q8. Why can a normal eye not see clearly objects placed closer than 25 cm?
Because 25 cm is the near point. To focus something nearer, the eye-lens would have to shorten its focal length below the minimum limit set by the ciliary muscles. Since it cannot, the image forms behind the retina and the object looks blurred.

Q9. What happens to the image distance in the eye when we increase the distance of an object from the eye?
The image distance stays essentially the same — the image always forms on the retina (fixed distance, ~2.3 cm). The eye keeps it there not by moving the image but by accommodation: as the object moves away, the eye-lens becomes thinner (focal length increases) to keep the image focused on the retina.

Q10. Why do stars twinkle?
Due to atmospheric refraction of starlight. The atmosphere has gradually changing refractive index; a star is a point source, so as the air's conditions fluctuate, the amount of starlight reaching the eye keeps varying — sometimes brighter, sometimes fainter — making the star appear to twinkle.

Q11. Explain why the planets do not twinkle.
Planets are much closer, so they appear as extended sources (many point sources). The variation in light from each point averages out to zero, so the total light entering the eye is steady — no twinkling.

Q12. Why does the sky appear dark instead of blue to an astronaut?
At high altitude there is no atmosphere to scatter sunlight. With no scattering, no blue light is sent towards the eye from all directions, so the sky looks dark instead of blue.

17. Common mistakes to avoid

• Swapping the corrections: myopia → concave, hypermetropia → convex. Mnemonic: myopia and concave.
• Forgetting signs in the lens formula — far point and near point distances are negative (virtual image, same side as object).
• Converting cm to m before using $P=\dfrac{1}{f}$; power is in dioptre only when $f$ is in metres.
• Saying "the lens does most of the refraction" — actually most refraction happens at the cornea; the lens only fine-tunes.
• Confusing dispersion order: violet bends most, red least (VIBGYOR, violet at the more-deviated end).
• Saying the Sun is red at sunset because it cools — it is because the blue is scattered away over the long atmospheric path.

18. Quick revision checklist

• Light path: cornea → aqueous humour → pupil → eye-lens → vitreous humour → retina → optic nerve → brain. Image is real & inverted.
• Accommodation = ciliary muscles changing lens curvature; near point 25 cm, far point infinity.
• Myopia → concave; hypermetropia → convex; presbyopia → bi-focal (concave top, convex bottom).
• $P=\dfrac{1}{f(\text{m})}$; concave $P<0$, convex $P>0$.
• Prism bends light to its base; disperses white light into VIBGYOR (red least, violet most). Rainbow = dispersion + total internal reflection in raindrops.
• Atmospheric refraction → twinkling of stars, advance sunrise/delayed sunset (~2 min); planets don't twinkle.
• Scattering → blue sky, red Sun at sunrise/sunset, dark sky for astronauts; Tyndall effect; red is least scattered.