In topic 2.3 you learnt what the defects are and where each one lands the image. Here you learn how to fix each one with a number: pick the right lens, then compute its focal length and power.
1. Present a worked example problem
Here is the kind of problem this whole lesson is built around. Read it once.
A person cannot see objects farther than 1.5 m clearly. (i) Name the defect. (ii) What kind of lens does she need? (iii) Find the focal length and power of the correcting lens.
That is it. One person, one prescription. By the end of this section you should be able to take any sentence like "cannot see beyond 1.5 m" or "near point is 1 m" and instantly know which symbol it becomes and what sign it carries.
Let me first recall the three defects in one line each, so the words in the problem mean something:
- Myopia (near-sightedness) — far objects blur; the image of a distant object lands in front of the retina. Far point has moved in from infinity. Fixed with a concave lens.
- Hypermetropia (far-sightedness) — near objects blur; the image of a near object would land behind the retina. Near point has moved out past 25 cm. Fixed with a convex lens.
- Presbyopia (ageing eye) — the eye loses its power of accommodation; near and far both blur. Fixed with a bifocal (concave above, convex below).
Stop scrolling. Try it in your head before reading on. The problem says "cannot see beyond 1.5 m." Near blur or far blur? Which of the three defects is that?
(Answer: far things blur, near things are fine → that is myopia. Her far point is 1.5 m instead of infinity.)
You can now match a "cannot see beyond X" sentence to its defect before touching any number.