When the image lands short
A student at the back cannot read the board. The book in the hand looks clear.
- This lens is too strong: parallel rays cross before the retina.
- A concave lens in front moves the crossing onto the retina.
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Slide the far point. Read the lens that fixes it.
The rule
Myopia is near-sightedness. Near objects look clear. Far objects blur. The far point is the farthest distance the eye sees sharply. In myopia it is closer than infinity.
Myopia has two causes. The eye lens may curve too much. Then it bends the rays too much. Or the eyeball may be too long.
In myopia, distant objects focus in front of the retina. A concave lens fixes it. The lens must put far objects at the far point.
A concave lens spreads the rays out. So they cross farther back, on the retina.
Worked example: far point 50 cm. The lens formula is 1/f = 1/v − 1/u. The letters are distances from the lens:
- u: the object distance.
- v: the image distance.
- f: the focal length.
A distance on the object's side is negative.
The lens must make far things look 50 cm away. Far things have 1/u = 0, so 1/f = 1/v and f = v. The image is on the object's side, so v = −50 cm. So f = −50 cm = −0.5 m. Power is in dioptres (D). Power = 1 ÷ f = 1 ÷ (−0.5) = −2 D.
The minus sign means a concave lens.
Watch out!
Power is 1 ÷ f with f in metres. Using centimetres gives the wrong power. Change 50 cm to 0.5 m first.