The Human Eye and the Colourful World
CBSE Class 10 · Science · Notes, formulas and practice questions
A revision guide to the human eye and the science of colour: how the eye focuses, why we need spectacles for myopia, hypermetropia and presbyopia, and how a prism, the atmosphere and tiny particles create the spectrum, twinkling stars, a blue sky and red sunrises.
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The human eye is like a camera: it collects light through the cornea, lets the iris control the amount entering, and uses the lens to focus a real, inverted image on the light-sensitive retina. The lens is flexible: the ciliary muscles change its curvature, changing its focal length so that objects from about 25 cm to infinity can be focused one after the other. This ability is called the power of accommodation.
When accommodation is defective, clear vision fails. In myopia (short-sightedness), the eye is too long or the lens too converging, so rays from a distant object meet before the retina; a concave lens of appropriate power corrects it. In hypermetropia (long-sightedness), the eyeball is too short or the lens too weak, so near objects focus behind the retina; a convex lens is needed. Presbyopia is the age-related loss of accommodation, commonly corrected with bifocal glasses.
The chapter also follows light through a prism. White light is a mixture of colours, and the refractive index of glass depends on wavelength. Violet is slowed most and red least, so each colour bends by a different amount at each surface of the prism; the emerging beam spreads out into a band of colours called the spectrum. This splitting is called dispersion. The order of colours, from lowest to highest deviation, is red, orange, yellow, green, blue, indigo, violet.
Many everyday phenomena in the sky are explained by refraction and scattering of light. The Earth's atmosphere is denser lower down, and light travelling through layers of changing density bends gradually. This atmospheric refraction makes stars appear to twinkle and brings the Sun into view a couple of minutes before actual sunrise. Tiny molecules preferentially scatter light of shorter wavelength: this is why the clear sky is blue and why the Sun at sunrise or sunset appears red, when its light passes through a thick layer of air.
Key terms
- Power of accommodation
- The ability of the eye lens to change its focal length by changing its curvature, so that images of objects at different distances are formed sharply on the retina.
- Near point and far point
- The near point is the closest distance at which the eye can clearly focus (about 25 cm for a normal adult). The far point is the greatest distance for clear vision; it is at infinity for a normal eye. The eye can accommodate objects anywhere between these two points.
- Myopia
- A defect in which a distant object is focused in front of the retina, so it appears blurred. It occurs when the eyeball is too long or the lens too curved, and is corrected with a concave (diverging) lens of suitable power.
- Hypermetropia
- A defect in which a nearby object is focused behind the retina, so near objects appear blurred. It occurs when the eyeball is too short or the lens too weak, and is corrected with a convex (converging) lens.
- Presbyopia
- An age-related defect in which the ciliary muscles weaken and the eye lens becomes rigid, reducing its power of accommodation. It usually makes near vision difficult and is often corrected with bifocal lenses.
- Dispersion
- The splitting of white light into its constituent colours when it passes through a prism. This occurs because the refractive index of the prism material is slightly different for every wavelength, so each colour is deviated by a different amount.
- Atmospheric refraction
- The gradual bending of light rays as they pass through air layers of different density (and hence different refractive index). This phenomenon causes twinkling of stars, advanced sunrise and delayed sunset.
- Scattering of light
- The redirection of light in many directions by tiny particles in the atmosphere. Shorter wavelengths (blue, violet) are scattered much more than longer wavelengths (red), which explains why the sky is blue and why the Sun appears red at sunrise and sunset.
- Tyndall effect
- The visible scattering of a light beam by colloidal particles whose size is comparable to the wavelength of light. It is seen when a headlight beam cuts through fog, or when a projector beam appears in a dusty cinema hall.
Formula sheet
| What | Formula | Notes |
|---|---|---|
| Power of a lens | P = 1/f | P is the power in dioptres (D) and f is the focal length in metres. A concave lens has negative power, a convex lens positive power. This is used to find the lens required to correct myopia or hypermetropia. |
| Lens formula (used in defect correction) | 1/f = 1/v − 1/u | u is the object distance (negative as per sign convention), v is the image distance (negative for a virtual image on the same side as the object), and f is the focal length. This allows calculation of the focal length of the corrective lens and hence its power. |
Practice questions with answers
1. State the power of accommodation of the human eye.
Power of accommodation is the ability of the eye lens to increase or decrease its curvature, and therefore change its focal length, so that clear images of objects placed at different distances are formed on the retina.
2. What is the near point of a normal human eye? What happens to the image on the retina when an object is brought closer than this point?
The near point of a normal eye is about 25 cm. If an object is placed closer than 25 cm, the ciliary muscles cannot make the lens thick enough to focus it, so even after maximum accommodation the image would form behind the retina and the object appears blurred.
3. A myopic person can see objects clearly only up to a distance of 1.2 m. What type of lens should be used to correct this defect, and what should be its focal length and power?
A concave lens is needed. For a myopic eye whose far point is at 1.2 m, the lens must have focal length f = −1.2 m so that rays from infinity appear to come from the far point. Its power is P = 1/f = 1/(−1.2) ≈ −0.83 D. Thus a concave lens of focal length 1.2 m and power −0.83 D is required.
4. A hypermetropic person has a near point at 50 cm. Calculate the power of the convex lens needed to read a book placed 25 cm away.
For the corrective lens, object distance u = −25 cm and the virtual image must form at the person's near point, v = −50 cm. Using the lens formula 1/f = 1/v − 1/u = 1/(−50) − 1/(−25) = −1/50 + 2/50 = 1/50, so f = +50 cm = 0.5 m. Power P = 1/0.5 = +2 D. Hence a convex lens of power +2 D (focal length 50 cm) is needed.
5. Why does a glass prism split white light into a spectrum?
White light is a mixture of colours of different wavelengths. The refractive index of the glass is slightly different for each wavelength — higher for violet than for red. So as white light enters and leaves the prism, each colour is deviated by a different angle, spreading the light into a continuous band of colours called the spectrum.
6. Why do stars twinkle at night, while a nearby planet such as Mars does not?
Stars are point sources so far away that their light passes through rapidly changing layers of the atmosphere; each layer refracts the light by a slightly different amount, causing the apparent position and brightness to fluctuate, making the star twinkle. A planet is an extended source — light from different points on its disc reaches the eye along many paths, and the fluctuations average out, so a planet shines steadily.
7. Explain why the clear sky appears blue, and why the Sun looks reddish at sunrise or sunset.
The sky appears blue because air molecules scatter shorter wavelengths (blue and violet) far more strongly than longer wavelengths. Our eye is more sensitive to blue, so the scattered light we see is predominantly blue. At sunrise and sunset, sunlight travels through a much thicker cross-section of atmosphere, and blue light is almost entirely scattered away from the line of sight, leaving the less-scattered red and orange colours to reach the eye, making the Sun look reddish.
8. What is the Tyndall effect? Give one example from everyday life.
The Tyndall effect is the scattering of light by colloidal particles that are large enough to scatter it in all directions, making the path of the light visible. It is seen when a car's headlight beam appears as a bright cone in fog, or when light passes through a glass of milk and becomes visible from the side.
9. What is presbyopia, and how is it usually corrected?
Presbyopia is an age-related defect in which the ciliary muscles become weak and the eye lens loses its flexibility, so the eye cannot focus on nearby objects. It is commonly corrected with bifocal lenses, in which the upper portion is used for distance vision and the lower portion for near vision. If no other defect exists, a single convex lens for reading may substitute.
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