Chapter 10: The Human Eye and the Colourful World

Q1: (b) accommodation. Q2: (d) retina. Q3: (c) 25 cm. Q4: (c) ciliary muscles.

f = 1/P. (i) Distant: f = 1/(−5.5) = −0.18 m = −18.2 cm (concave lens). (ii) Near: f = 1/(+1.5) = +0.67 m = +66.7 cm (convex lens).

A concave lens is needed with focal length equal to the far point: f = −80 cm = −0.8 m. P = 1/f = 1/(−0.8) = −1.25 D.

Corrected by a convex lens. Object at 25 cm should appear at the near point 100 cm: u = −25 cm, v = −100 cm. 1/f = 1/v − 1/u = −1/100 + 1/25 = 3/100 → f = 100/3 = 33.3 cm = 0.33 m. P = 1/0.33 = +3 D.

Q8: 25 cm is the near point (least distance of distinct vision). For closer objects the ciliary muscles cannot make the lens thick (short) enough, so the image is not focused on the retina. Q9: The image distance stays the same — the image always forms on the retina (a fixed distance). Only the focal length of the lens changes (via accommodation).

Q10: Stars twinkle due to atmospheric refraction — starlight bends by varying amounts as it passes through air layers of changing density, so the star's apparent position and brightness keep fluctuating. Q11: Planets are much closer and act as a collection of many point sources (an extended source); the variations from different points average out, so their light stays steady — no twinkling.

Because in space there is no atmosphere (no air molecules) to scatter sunlight. On Earth, scattering of light by air makes the sky look blue; without it, the sky appears dark.

Red.

Inverted (the brain interprets it as erect).

Presbyopia.

Spectrum.

Concave lens f = −50 cm = −0.5 m; P = 1/(−0.5) = −2 D.

u=−25, v=−40. 1/f = −1/40 + 1/25 = (−5+8)/200 = 3/200 → f = 66.7 cm = 0.667 m; P = +1.5 D.

f = 1/(−4) = −0.25 m = −25 cm (concave).

f = 1/2.5 = 0.4 m = 40 cm (convex).

The splitting of white light into its seven constituent colours when it passes through a prism.

Air molecules scatter blue light (shorter wavelength) more than other colours, so the sky looks blue.

The scattering of light by very fine particles (colloids) in its path, making the path visible.

Myopia (near-sightedness) is the inability to see distant objects clearly. The image forms in front of the retina, either because the eyeball is too long or the lens is too converging. It is corrected using a concave (diverging) lens that moves the image back onto the retina.

Hypermetropia (far-sightedness) is the inability to see nearby objects clearly. The image forms behind the retina, because the eyeball is too short or the lens too weak. It is corrected using a convex (converging) lens that brings the image onto the retina.

At sunrise/sunset, sunlight travels through a thicker layer of atmosphere. Blue and shorter wavelengths are scattered away, and mainly the red light (least scattered) reaches our eyes, so the sun looks red.

Light enters through the cornea and pupil (size controlled by the iris), is focused by the eye lens (adjusted by ciliary muscles) onto the retina, which forms a real, inverted image. The retina sends signals through the optic nerve to the brain, which interprets the image.