Class 10 › Science › Chapter 10
The Human Eye and the Colourful World
Structure of the eye, accommodation, defects of vision and their correction, refraction through a prism, dispersion and rainbow, atmospheric refraction and scattering of light.
1. The Human Eye
- The eye works like a camera: its lens system forms a real, inverted image on a light-sensitive screen, the retina. Eyeball diameter is about 2.3 cm.
| Part | Function |
|---|---|
| Cornea | Thin transparent bulge at the front; most refraction of light entering the eye occurs at its outer surface |
| Iris | Dark muscular diaphragm that controls the size of the pupil |
| Pupil | Regulates the amount of light entering the eye |
| Eye lens (crystalline) | Fine adjustment of focal length to focus objects at different distances on the retina |
| Ciliary muscles | Change the curvature (and focal length) of the lens |
| Retina | Delicate membrane with enormous numbers of light-sensitive cells; they make electrical signals sent through the optic nerves to the brain, which interprets them |
2. Power of Accommodation
Accommodation: the ability of the eye lens to adjust its focal length to focus on near and distant objects.
Distant objects
Muscles relax
Lens becomes thin; focal length increases.
Near objects
Muscles contract
Lens becomes thick (more curvature); focal length decreases.
| Point | Meaning | Normal eye |
|---|---|---|
| Near point (least distance of distinct vision) | Minimum distance at which objects are seen most distinctly without strain | about 25 cm |
| Far point | Farthest point up to which the eye sees clearly | Infinity |
- A normal eye sees clearly between 25 cm and infinity. It cannot see objects closer than 25 cm clearly because the focal length of the lens cannot be decreased below a minimum limit.
- When an object moves farther, the image distance in the eye stays the same (on the retina); the lens adjusts its focal length instead.
- Cataract: the lens of old people becomes milky and cloudy, causing partial or complete loss of vision; restored by surgery.
3. Defects of Vision and their Correction
| Myopia (near-sightedness) | Hypermetropia (far-sightedness) | Presbyopia | |
|---|---|---|---|
| Can see clearly | Nearby objects | Distant objects | Distant (near vision difficult) |
| Problem | Far point is nearer than infinity; image of a distant object forms in front of the retina | Near point is farther than 25 cm; image of a near object forms behind the retina | Near point gradually recedes with age |
| Causes | Excessive curvature of the lens, or elongated eyeball | Focal length of lens too long, or eyeball too small | Weakening of ciliary muscles and loss of lens flexibility |
| Correction | Concave lens of suitable power | Convex lens of suitable power | Corrective lenses; bi-focal if combined with myopia or hypermetropia |
- Bi-focal lens: upper part concave (distant vision), lower part convex (near vision).
- Refractive defects can also be corrected by contact lenses or surgery.
- A student who cannot read the blackboard from the last row has myopia; correct with a concave lens.
- Eye donation: any age or sex can donate; spectacle wearers and cataract-operated people can donate; eyes must be removed within 4 to 6 hours of death; one pair can give vision to up to four corneal-blind people.
4. Calculating the Correcting Lens (Numericals)
Method
Myopia: the lens must form a virtual image of a far object at the far point. Take u = ∞ and v = −(far point); then f = −(far point distance), so P = −1/(far point in m).
Hypermetropia: the lens must form a virtual image of an object at 25 cm at the person's near point. u = −25 cm, v = −(near point); use 1/f = 1/v − 1/u.
Use P = 1/f with f in metres (dioptre).
| Problem | Working | Answer |
|---|---|---|
| Myopic eye cannot see beyond 1.2 m | f = −1.2 m; P = −1/1.2 | Concave lens, ≈ −0.83 D |
| Far point 80 cm | f = −0.8 m; P = −1/0.8 | Concave, −1.25 D |
| Hypermetropic eye, near point 1 m | 1/f = 1/(−100) − 1/(−25) = 3/100 → f = +33.3 cm | Convex, +3.0 D |
| Lens of −5.5 D (distant) and +1.5 D (near) | f = 1/P | −0.18 m (≈ −18 cm); +0.67 m (≈ 67 cm) |
5. Refraction of Light through a Prism
- A triangular prism has two triangular bases and three rectangular lateral faces. The angle of the prism (∠A) is the angle between its two refracting lateral faces.
- At the first face (air to glass) the ray bends towards the normal; at the second face (glass to air) it bends away from the normal.
- Because the faces are inclined (not parallel), the emergent ray is not parallel to the incident ray. The angle between them is the angle of deviation (∠D).
- Terms: ∠i angle of incidence, ∠r angle of refraction, ∠e angle of emergence; rays: incident (PE), refracted (EF), emergent (FS).
Slab vs prism: a rectangular slab only shifts the ray sideways (emergent parallel to incident); a prism deviates it by an angle.
6. Dispersion of White Light and the Rainbow
Dispersion: splitting of white light into its component colours. The band of colours is the spectrum. Order: VIBGYOR (Violet, Indigo, Blue, Green, Yellow, Orange, Red).
- Why? Different colours bend through different angles in a prism: red bends the least, violet the most.
- Newton first obtained the spectrum of sunlight with a prism. A second identical prism placed inverted recombined the colours into white light, showing that sunlight is made of seven colours.
Rainbow formation
A rainbow is a natural spectrum seen after rain, formed by tiny water droplets acting like small prisms.
Sunlight is refracted and dispersed on entering a drop, internally reflected, then refracted again on leaving. Different colours reach the observer's eye.
A rainbow always forms in the direction opposite to the Sun (Sun behind the observer). Also seen through a waterfall or fountain.
7. Atmospheric Refraction
Atmospheric refraction: refraction of light by the earth's atmosphere, whose refractive index changes gradually (and keeps varying).
Wavering
Hot air flicker
Hot air is lighter (less dense) with slightly lower refractive index; its changing conditions make objects seen through it appear to waver.
Twinkling of stars
Fluctuating path
Starlight refracts continuously, bending towards the normal, so the star appears slightly higher; the apparent position fluctuates, so the amount of light entering the eye flickers (brighter, then fainter). Stars are point-sized sources.
Planets do not twinkle
Extended sources
Planets are closer and act as many point sources; the variations average out to zero.
Sunrise and sunset
About 2 minutes
The Sun is visible about 2 minutes before actual sunrise and 2 minutes after actual sunset. This also flattens the Sun's disc near the horizon.
8. Scattering of Light
Tyndall effect: scattering of light by colloidal (or fine suspended) particles, which makes the path of a beam visible (sunlight through smoke-filled room or forest canopy mist).
- Colour of scattered light depends on the size of the particles: very fine particles scatter mainly blue; larger particles scatter longer wavelengths; if large enough, scattered light appears white.
Why is the clear sky blue?
Air molecules and fine particles are smaller than the wavelength of visible light, so they scatter shorter wavelengths (blue) far more than longer wavelengths (red). Red light's wavelength is about 1.8 times that of blue.
The scattered blue light reaches our eyes, so the sky looks blue.
No atmosphere (or very high altitude): no scattering, so the sky looks dark to an astronaut or to passengers at great heights.
- Danger signals are red because red is least scattered by fog or smoke, so it stays visible from far away.
- Colour of deep sea water and reddening of the Sun at sunrise and sunset are also due to scattering.
9. Quick Revision
| Phenomenon | Cause |
|---|---|
| Image formed on retina | Refraction at cornea + eye lens (accommodation by ciliary muscles) |
| Myopia / hypermetropia | Image formed in front of / behind the retina |
| Spectrum from a prism | Different colours bend by different angles (violet most, red least) |
| Rainbow | Dispersion + internal reflection in raindrops |
| Twinkling of stars | Atmospheric refraction of starlight |
| Blue sky | Scattering of short wavelengths by fine air particles |
| Red danger signal | Red is scattered least |
Common mistakes:
• Mixing up myopia (concave lens, distant objects blurred) with hypermetropia (convex lens, near objects blurred).
• Saying the eye lens does most of the refraction; the cornea does, the lens only fine-tunes.
• Saying violet bends least; red bends least.
• Saying the emergent ray from a prism is parallel to the incident ray (true for a slab).
• Saying planets twinkle, or that stars twinkle due to their own flickering; it is atmospheric refraction.
• Forgetting to put the far point in metres and the sign (negative) in the power of a myopic lens.
• Saying the sky is blue because of reflection from the sea.
• Mixing up myopia (concave lens, distant objects blurred) with hypermetropia (convex lens, near objects blurred).
• Saying the eye lens does most of the refraction; the cornea does, the lens only fine-tunes.
• Saying violet bends least; red bends least.
• Saying the emergent ray from a prism is parallel to the incident ray (true for a slab).
• Saying planets twinkle, or that stars twinkle due to their own flickering; it is atmospheric refraction.
• Forgetting to put the far point in metres and the sign (negative) in the power of a myopic lens.
• Saying the sky is blue because of reflection from the sea.