Defects of the eye and their correction

An optician prescribes lenses of power $-2.5\text{ D}-2.5\backslash \; \backslash text\{D\}$ for a student. What kind of lens is it, what is its focal length, and what defect does she have?

1. Sign: the power is negative, so the lens is diverging (concave).
2. Focal length: $f=\frac{1}{P}=\frac{1}{-2.5}=-0.4\text{ m}f\; =\; \backslash frac\{1\}\{P\}\; =\; \backslash frac\{1\}\{-2.5\}\; =\; -0.4\backslash \; \backslash text\{m\}$, that is, 40 cm (negative because it is diverging).
3. Defect: a diverging lens corrects myopia, so she is short-sighted: the board is blurred, her book is clear.
4. A lens of $+2.0\text{ D}+2.0\backslash \; \backslash text\{D\}$ would be converging, with $f=\frac{1}{2.0}=0.5\text{ m}f\; =\; \backslash frac\{1\}\{2.0\}\; =\; 0.5\backslash \; \backslash text\{m\}$, for hypermetropia or presbyopia.

1. A man of 62 sees the hills clearly but holds his phone at arm's length to read it. His distance vision is fine, and the problem began in middle age: presbyopia, a lens that has lost its elasticity. Convex reading glasses.
2. A woman of 70 says everything looks as though she is seeing it through mist, and car headlights dazzle her. A cloudy lens: cataract. Surgery to replace the lens.
3. A boy cannot tell red from green apples by colour, although he sees their shapes perfectly. Faulty red- or green-sensitive cones: colour blindness. No cure; he can learn other clues, such as shade and position.