Class 10 · CBSE / NCERT · Physics

The Human Eye and the Colourful World — Class 10

Why is the sky blue and the sunset red? Why do some people need glasses? Learn the eye and its defects, and compute the power of the correcting lens.

AccommodationThe ability of the eye lens to change its focal length (via ciliary muscles) to focus on near and distant objects. Least distance of distinct vision = 25 cm.

Myopia (short-sightedness)Can see near objects but not distant ones; the image forms in front of the retina. Corrected with a concave (diverging) lens.

Hypermetropia (long-sightedness)Can see distant objects but not near ones; the image forms behind the retina. Corrected with a convex (converging) lens.

Dispersion & scatteringA prism splits white light into 7 colours (dispersion). Scattering of blue light by air molecules makes the sky blue and the setting sun red.

Lens power calculator Interactive

Enter the focal length to find the power of a lens (use a minus sign for a concave/diverging lens).

Focal length magnitude (f) 50 cm

Power, P = 1/f—D

A concave lens (for myopia) has NEGATIVE power; a convex lens (for hypermetropia) has POSITIVE power.

Numericals practice Interactive

Lens power and defect-correction problems with steps.

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Solved numericals

Q1. A person cannot see objects nearer than 50 cm. What is the power of the lens needed to read at the normal 25 cm?

Hypermetropia: use a convex lens. u = −25 cm, v = −50 cm (virtual image at his near point)

1/f = 1/v − 1/u = −1/50 + 1/25 = 1/50 ⇒ f = +50 cm

P = 100/50 = +2 D

Q2. Why does the sky appear blue?

Sunlight is scattered by air molecules.

Blue light (shorter wavelength) is scattered much more than red light.

So the scattered light reaching our eyes from all directions is mostly blue.

Formula sheet

Quantity	Formula	SI unit
Power of a lens	P = 1 / f (metres)	dioptre (D)
Myopia correction	f = − (far point distance)	concave, P negative
Hypermetropia correction	convex lens	P positive
Least distance of distinct vision	D = 25 cm	cm

Common mistakes & exam wins

Least distance of distinct vision for a normal eye is 25 cm.
Myopia → concave lens (−P); Hypermetropia → convex lens (+P).
The colour of scattered light depends on wavelength — blue scatters most, red least (so danger signals are red).
At sunrise/sunset light travels through more atmosphere, blue is scattered away, so the Sun looks red.

Frequently asked questions

What is the least distance of distinct vision?

The closest distance at which the eye can see an object clearly without strain — about 25 cm for a normal adult eye.

How is myopia corrected?

With a concave (diverging) lens of suitable focal length, which moves the image back onto the retina.

Why does the sky appear blue but the setting sun red?

Air scatters short-wavelength blue light strongly, making the sky blue. At sunset the light crosses more air, blue is scattered away, and mostly red reaches us.

What is dispersion of light?

The splitting of white light into its seven constituent colours (VIBGYOR) when it passes through a prism, because each colour bends by a different amount.