9 min readConcept sheetOften a 5-mark answer with ray diagrams of the defect and its correction; lens power numericals come as 2-mark or 3-mark questions

Defects of vision and their correction

In myopia far objects blur and a concave lens corrects it. In hypermetropia near objects blur and a convex lens corrects it. Presbyopia comes with age.

Myopia (near-sightedness)Image of a far object forms in front of the retina; concave lens

Hypermetropia (far-sightedness)Image of a near object forms behind the retina; convex lens

PresbyopiaNear point moves away with age

Bifocal lensUpper part concave (far vision), lower part convex (reading)

Myopia vs hypermetropia

Myopia (near-sightedness)Sees near objects clearly, but distant ones blur. The far point comes closer than infinity. The image of a far object forms in front of the retina. Causes: the eye lens is too curved, or the eyeball is too long. Corrected by a concave (diverging) lens of suitable power.

Hypermetropia (far-sightedness)Sees distant objects clearly, but near ones blur. The near point moves farther than 25 cm. The image of a near object forms behind the retina. Causes: the focal length of the eye lens is too long, or the eyeball is too small. Corrected by a convex (converging) lens of suitable power.

Memory: myopia needs a minus lens (concave, negative power). Hypermetropia needs a plus lens (convex, positive power).

Presbyopia and bifocal lenses

Presbyopia means the power of accommodation becomes weaker with age.
The near point slowly moves away, so many older people find it hard to read small print without glasses.
Causes: the ciliary muscles gradually weaken and the eye lens becomes less flexible.
It is corrected with a convex lens for near work.
Some people have both myopia and hypermetropia. They use bifocal lenses: the upper part is concave for distant vision and the lower part is convex for reading.
Today, these defects can also be corrected with contact lenses or by surgery.

How to draw myopia and its correction

Draw three small figures, one below the other. In each, draw the eye as a circle with a lens near the front and the retina at the back. Draw a straight axis through the middle.

1
(a) Far point of a myopic eye: mark the far point O on the axis a short distance in front of the eye. Draw rays from O that meet on the retina. Label 'far point O'.
2
(b) Myopic eye: draw parallel rays from a distant object (at infinity) entering the eye. Make them meet at a point in front of the retina. Label 'image in front of the retina'.
3
(c) Correction: draw a concave lens in front of the eye. The parallel rays spread out after it, as if they came from O (show dotted lines back to O). Now the eye lens brings them together on the retina.
The concave lens must have a focal length equal to the far point distance.
4
Label each figure: myopic eye, far point O, concave lens, retina.

How to draw hypermetropia and its correction

1
(a) Near point of a hypermetropic eye: mark N′, the normal near point, at 25 cm. Mark N, the near point of this eye, farther away on the axis. Draw rays from N that meet on the retina. This eye cannot see an object at N′ clearly.
2
(b) Hypermetropic eye: draw rays from an object at N′ entering the eye. Make them meet at a point behind the retina (carry the lines past the retina to a point). Label 'image behind the retina'.
3
(c) Correction: draw a convex lens in front of the eye. Rays from N′ bend inwards after it, as if they came from N (show dotted lines back to N). Now the eye lens brings them together on the retina.
4
Label each figure: hypermetropic eye, N (near point of this eye), N′ (normal near point), convex lens, retina.

Finding the power of a corrective lens

Problem

(a) A myopic person's far point is 40 cm. Find the power of the lens needed to see distant objects. (b) A hypermetropic person's near point is 50 cm. Find the power of the lens needed to read a book held at 25 cm. (Take the lens to be close to the eye.)

Working

(a) The lens must make a very distant object (u = −∞, so 1/u = 0) appear at the far point: v = −40 cm.
Lens formula: 1/f = 1/v − 1/u = 1/(−40) − 0, so f = −40 cm = −0.40 m.
P = 1/f = 1/(−0.40 m) = −2.5 D.
(b) The lens must make an object at u = −25 cm appear at the near point: v = −50 cm.
1/f = 1/v − 1/u = −1/50 + 1/25 = (−1 + 2)/50 = 1/50, so f = +50 cm = +0.50 m.
P = 1/f = 1/(0.50 m) = +2 D.

Answer

(a) A concave lens of power −2.5 D. (b) A convex lens of power +2.0 D.

In real life

Many grandparents wear bifocals: the top part for watching TV, the bottom part for reading the newspaper. A child who must move to the front bench to read the board needs an eye test, as myopia is easily corrected.

Exam angle

2 marks: “Name the defect of vision in which the image of a distant object forms in front of the retina. Give two causes of it.” Myopia. Causes: too much curvature of the eye lens, or an elongated eyeball.

3 marks: “The near point of a hypermetropic eye is 1.5 m. What kind of lens is needed to read at 25 cm? Find its power.” Convex lens. u = −25 cm, v = −150 cm; 1/f = −1/150 + 1/25 = 5/150 = 1/30; f = +30 cm = 0.30 m; P = 1/0.30 ≈ +3.3 D (rounded).

5 marks: “What is myopia? Give two causes. Draw ray diagrams to show a myopic eye and its correction.” Definition; two causes; three figures: far point O, image in front of the retina, and a concave lens making parallel rays seem to come from O.

Remember it

Myopia: minus lens (concave). Hypermetropia: plus lens (convex). Presbyopia: comes with age, often with bifocals.