Chapter 10: The Human Eye and the Colourful World (Physics)

It is the ability of the eye lens to change its focal length (through the ciliary muscles) so that both near and distant objects are focused sharply on the retina.

The ability of the eye lens to adjust its focal length to see near and far objects clearly.

The far point of the eye is 1.2 m, so a concave (diverging) lens is needed. It must form a virtual image at 1.2 m of an object at infinity, so its focal length is $f=-1.2$ m and $P=\frac{1}{-1.2}\approx -0.83$ D.

A concave lens (of focal length −1.2 m, power about −0.83 D).

Far point: infinity. Near point: about 25 cm from the eye.

The student can see near objects but not distant ones, so the defect is myopia (near-sightedness). The image of a distant object forms in front of the retina. It is corrected with spectacles having a concave lens of suitable power, which diverges the rays so the image forms on the retina.

Myopia; it is corrected with a concave lens of suitable power.

(b) accommodation

(d) retina

(c) 25 cm

(c) ciliary muscles

1. $f=\frac{1}{P}=\frac{1}{-5.5}\approx -0.182$ m $=-18.2$ cm (a concave lens)
2. $f=\frac{1}{1.5}\approx 0.667$ m $=+66.7$ cm (a convex lens)

(i) −18.2 cm (ii) +66.7 cm

The lens must form, at the far point, a virtual image of an object at infinity: $u=-\infty$, $v=-80$ cm, so $f=-80$ cm $=-0.8$ m.

$P=\frac{1}{-0.8}=-1.25$ D

A concave lens of power −1.25 D.

The lens must form a virtual image at the eye's near point (1 m) of an object at 25 cm: $u=-25$ cm, $v=-100$ cm.

$$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}=-\frac{1}{100}+\frac{1}{25}=\frac{3}{100}\Rightarrow f=\frac{100}{3}\text{ cm}=\frac{1}{3}\text{ m}$$

$P=\frac{1}{1/3}=+3$ D

A convex lens of power +3 D.

To focus a nearby object, the ciliary muscles make the eye lens thicker, which reduces its focal length. The focal length cannot be reduced below a certain limit. For objects closer than 25 cm, the lens cannot become any thicker, so the image is formed behind the retina and looks blurred (and the eye strains).

Because the eye lens cannot reduce its focal length beyond a limit, so such objects cannot be focused on the retina.

Nothing: the image distance stays the same, because the image must always form on the retina, at a fixed distance from the eye lens. What changes is the focal length of the eye lens, which increases (the lens becomes thinner) through accommodation.

The image distance remains the same; the eye lens adjusts its focal length instead.

Starlight passes through layers of the atmosphere whose temperature and density keep changing, so their refractive index keeps changing. The light from a star is therefore refracted by varying amounts (atmospheric refraction). Because a star is so far away, it behaves like a point source, and the slight changes make its apparent position and the amount of light entering our eyes flicker. The star then looks brighter at one moment and fainter at the next: it twinkles.

Changing atmospheric refraction makes the light from these point-like sources flicker in position and brightness.

Planets are much closer to the Earth, so they look like extended sources (tiny discs) rather than points. A planet can be treated as many point sources. The variations in light from the different points average out, so the total light reaching our eyes stays steady, and planets do not twinkle.

Planets are extended sources, so the flickering of light from their many points cancels out.

The blue colour of the sky is due to the scattering of sunlight (mainly blue light) by the molecules and fine particles of the atmosphere. At very high altitudes, above the atmosphere, there is no air to scatter sunlight, so no light is scattered towards the astronaut's eyes, and the sky looks dark.

Above the atmosphere there are no particles to scatter sunlight, so the sky looks dark.