The Human Eye and the Colourful World

How the eye focuses, the common defects of vision and the lenses that correct them, and why light splits, bends and scatters in the atmosphere.

Key ideas

The cornea does most of the bending of light; the eye lens fine-tunes the focus to form a real, inverted image on the retina.
Accommodation: the ciliary muscles change the focal length of the eye lens. A normal eye sees clearly from about 25 cm (near point) to infinity (far point).
Myopia (short sight): distant objects blur because the image forms in front of the retina; a concave lens corrects it.
Hypermetropia (long sight): nearby objects blur because the image forms behind the retina; a convex lens corrects it. Presbyopia is the same problem with age; bifocals help.
A prism splits white light into VIBGYOR (dispersion): violet bends the most, red the least.
Atmospheric refraction makes stars twinkle and lets us see the sun about 2 minutes before sunrise and after sunset.
Small particles scatter blue light more than red: the sky is blue, sunsets are red, and danger signals are red.

Remember

Lens for myopia (far point F)	concave, f = −F
Lens for hypermetropia (near point N)	1/f = 1/25 − 1/N (in cm)
Power of a lens	P = 1 ÷ f (in metres) = 100 ÷ f (in cm), in dioptres
Order of colours	violet, indigo, blue, green, yellow, orange, red

Watch out

Giving a convex lens for myopia (it needs a concave lens with negative power).
Leaving the focal length in cm when finding power: use metres, or P = 100 ÷ f (cm).
Saying red bends the most in a prism (violet does).
Calling twinkling of stars "scattering" (it is atmospheric refraction).

Worked example

Zoya sits at the back of the class and cannot read the board, which is farther than 5 m, but can read a book easily. (a) Name the defect. (b) Give two possible causes. (c) Find the type, focal length and power of the lens needed.

Working: the image of a distant object forms in front of the retina; the lens must give a virtual image at 500 cm

Answer: (a) myopia; (b) the eyeball is too long, or the eye lens is too curved; (c) concave, f = −500 cm, P = −0.2 D