The Human Eye and the Colourful World — Problems & Practice

Chapter 10 | NCERT Class 10 Science

Original practice inspired by NCERT / board style. Full solutions included. Not verbatim textbook exercises.

Easy

Problem 1

What is meant by power of accommodation of the eye?

Solution: It is the ability of the eye lens to adjust its focal length (by action of ciliary muscles) so that both nearby and distant objects can be focused clearly on the retina.

Problem 2

A student in the last row cannot read the blackboard clearly but can read a book held nearby. Name the defect and the type of lens required.

Solution: Myopia (near-sightedness). Corrected by a concave lens of suitable power.

Problem 3

Why is a normal eye unable to see clearly objects closer than about $25$ cm?

Solution: The focal length of the eye lens cannot be decreased below a certain minimum. Objects closer than the near point ( $\approx 25$ cm) cannot be focused distinctly on the retina without strain.

Problem 4

State the sequence of colours in the spectrum of white light obtained with a glass prism.

Solution: Violet, Indigo, Blue, Green, Yellow, Orange, Red (VIBGYOR).

Medium

Problem 5

The far point of a myopic person is $100$ cm in front of the eye. Find the nature and power of the lens required to correct the defect.

Solution: Need image of a distant object at the far point: $u = - \infty$ , $v = - 1.00$ m. $\frac{1}{f} = \frac{1}{v} - \frac{1}{u} = - 1 \Rightarrow f = - 1 m, P = - 1.0 D$ Concave lens of power $- 1.0$ D.

Problem 6

A person needs a lens of power $- 4.0$ D for distant vision and $+ 1.5$ D for near vision. Find the focal lengths of the two lenses.

Solution: Distant: $f_{1} = 1/ P_{1} = 1/ (- 4.0) = - 0.25$ m.
Near: $f_{2} = 1/ (+ 1.5) = + \frac{2}{3} m \approx + 0.67$ m.

Problem 7

Explain why stars twinkle but planets do not.

Solution: Starlight is continuously refracted by a changing atmosphere, so a star’s apparent position and brightness fluctuate (point source). Planets are closer and appear as extended sources; light from many points averages out fluctuations, so they do not twinkle.

Problem 8

Why does the sky appear dark to an astronaut in space, instead of blue?

Solution: There is no (or negligible) atmosphere to scatter sunlight. Without scattering of shorter wavelengths, the sky does not appear blue and looks dark.

Hard

Problem 9

The near point of a hypermetropic eye is $1.0$ m. What is the power of the lens needed so that the person can read at $25$ cm? Assume normal near point is $25$ cm.

Solution: Object at $u = - 0.25$ m; virtual image at near point $v = - 1.0$ m. $\frac{1}{f} = \frac{1}{v} - \frac{1}{u} = - 1 - \frac{1}{- 0.25} = - 1 + 4 = + 3$ $P = + 3.0 D$ (convex lens).

Problem 10

A person uses bifocal lenses. The far point of the myopic eye is $40$ cm. For near vision, the near point is $50$ cm (normal near point taken as $25$ cm). Find the powers of both:

(a) the upper (distant-vision) lens, and
(b) the lower (near-vision) lens.

Solution: (a) Distant (upper) lens — myopia correction
Need image of a distant object at the far point: $u = - \infty$ , $v = - 0.40$ m. $P_{upper} = \frac{1}{f} = \frac{1}{v} - \frac{1}{u} = - \frac{1}{0.40} = - 2.5 D$ Upper part is a concave lens of power $- 2.5$ D.

(b) Near (lower) lens — near-vision correction
Object at the normal near point $u = - 0.25$ m; virtual image at the person’s near point $v = - 0.50$ m. $\frac{1}{f} = \frac{1}{v} - \frac{1}{u} = \frac{1}{- 0.50} - \frac{1}{- 0.25} = - 2 + 4 = + 2$ $P_{lower} = + 2.0 D$ Lower part is a convex lens of power $+ 2.0$ D.

Final answer: Upper $- 2.5$ D (concave); lower $+ 2.0$ D (convex).

Problem 11

(a) What is dispersion? (b) Why does violet light deviate more than red in a prism? (c) How is a rainbow formed?

Solution: (a) Splitting of light into its component colours.
(b) Different colours travel at slightly different speeds in glass, so they refract by different amounts; violet bends more than red.
(c) Sunlight is dispersed and internally reflected by water droplets opposite the Sun; different colours reach the observer’s eye as a spectrum.

Self-check

If you missed…	Revisit
Wrong correcting lens	Defect table in §10.2
Power sign/magnitude	Far/near point as $v$
Twinkling vs planets	Atmospheric refraction
Sky colour	Scattering of short wavelengths
Rainbow direction	Opposite the Sun