The Human Eye and the Colourful World — Important Questions

Answer: (a) Ciliary muscles - they change the curvature of the eye lens, altering its focal length. This ability of the eye is called the power of accommodation.

Answer: (a) Myopia; concave lens - in myopia the image of a distant object forms in front of the retina, so a concave (diverging) lens of suitable power pushes the image back onto the retina.

Answer: (a) Scattered the most as it has a shorter wavelength - by Rayleigh scattering the scattered intensity is $\propto \frac{1}{\lambda^4}$, so shorter-wavelength blue light is scattered far more than red, making the sky look blue.

Answer: (a) $-0.5\ \text{D}$ - the concave lens must have its focus at the far point, so $f=-2\ \text{m}$ and $P=\frac{1}{f}=\frac{1}{-2}=-0.5\ \text{D}$. The negative sign confirms a concave lens.

Answer: (a) Both A and R are true and R is the correct explanation of A - the blue colour of the sky is due to the scattering of sunlight by air molecules. Where there is no atmosphere the light is not scattered, so the sky appears dark except where the Sun and stars are seen.

At sunrise and sunset the Sun is near the horizon, so sunlight travels through a greater thickness of the atmosphere to reach us. Most of the shorter-wavelength blue light is scattered away along this long path, and mainly the longer-wavelength red light reaches our eyes, so the Sun appears reddish. At noon the Sun is overhead, the path is shortest, least scattering occurs and it appears nearly white.

The phenomenon is the twinkling of stars, caused by the atmospheric refraction of starlight. Because the physical conditions (temperature and density) of the atmosphere keep changing, the amount of bending of the star's light keeps changing, so the apparent position and apparent brightness of the star fluctuate and the star seems to twinkle. Planets do not twinkle because, being much closer, they act as extended sources of light.

(a) Myopia (near-sightedness).
(b) It may be caused by (i) excessive curvature of the cornea/eye lens, or (ii) elongation of the eyeball, so that parallel rays from a distant object converge in front of the retina.
(c) A concave (diverging) lens of suitable focal length is used. It diverges the incoming parallel rays before they enter the eye so that they finally focus on the retina (see the diagram).

(a) Hypermetropia (far-sightedness) is a defect in which a person can see distant objects clearly but cannot see nearby objects distinctly; the image of a nearby object forms behind the retina and the near point is farther than 25 cm.
(b) It is caused by (i) the focal length of the eye lens being too long (low converging power), or (ii) the eyeball being too short.
(c) It is corrected with a convex (converging) lens of suitable power. The convex lens adds the converging power the eye lacks, so the image of a nearby object is brought forward exactly onto the retina.

(a) Red light has the longest wavelength among visible colours, so it is scattered the least by fog, dust and smoke and can travel the largest distance without much loss. It is therefore easily visible from far away and is used for danger/stop signals.
(b) Air molecules scatter the shorter-wavelength blue light much more than red (scattered intensity $\propto \frac{1}{\lambda^4}$). The scattered blue light reaching our eyes from all directions makes the sky look blue.
(c) In space (or at very high altitudes) there is no atmosphere, hence no scattering of sunlight, so the sky appears dark/black except where the Sun and stars are seen.

(a) For distant vision the defect is myopia; for near vision it is hypermetropia (together they indicate presbyopia).
(b) Distant vision needs a concave (diverging) lens (negative power); near vision needs a convex (converging) lens (positive power).
(c) Using $P=\frac{1}{f}$ so that $f=\frac{1}{P}$ (in metres):
For distant vision, $f=\frac{1}{-4.5}=-0.22\ \text{m}=-22.2\ \text{cm}$ (concave).
For near vision, $f=\frac{1}{+1.5}=+0.67\ \text{m}=+66.7\ \text{cm}$ (convex).
(d) A bifocal lens has two parts in each glass: the upper concave part corrects distant vision and the lower convex part corrects near vision, so a single pair of spectacles serves both needs.

(a) Dispersion is the splitting of white light into its seven constituent colours (VIBGYOR - violet, indigo, blue, green, yellow, orange, red) on passing through a prism.
(b) See the diagram: a narrow beam of white light entering the prism emerges as a band of seven colours, with red deviated least and violet most.
(c) Different colours have different wavelengths and travel with different speeds in glass, so each is refracted through a different angle. Violet (shortest wavelength) is slowed the most and bends the most; red (longest wavelength) bends the least.
(d) Newton placed a second, identical but inverted prism in the path of the spectrum from the first prism. The seven colours recombined to give white light, proving that white light is a mixture of seven colours.

(i) Myopia (near-sightedness) - he cannot see distant objects (the blackboard) clearly.
(ii) A concave (diverging) lens of suitable power.
(iii) The grandfather suffers from presbyopia, corrected using bifocal lenses (a concave upper part for distant vision and a convex lower part for near vision).
(iv) With age the ciliary muscles weaken and the eye lens loses its flexibility, so the power of accommodation decreases and the near point recedes.