Question

A woman can read the large print in a newspaper only when it is at a distance of 55 cm or more from her eyes.
(a) Is she nearsighted (myopic) or farsighted (hyperopic), and what kind of lens is used in her glasses to correct her eyesight?
(b) What should be the refractive power (in diopters) of her glasses (worn 2.7 cm from the eyes), so she can read the newspaper at a distance of 22 cm from the eyes?

Answer 1

Answer:

Farsightedness (hyperopic)

2.79 D

Explanation:

When a person cannot see something which is close to their eyes this condition is known as farsightedness. She should use a convex lens to correct her eye sight.

u = Object distance =  22-2.7 = 19.3 cm

v = Image distance = -55+2.7 = -52.3 cm

f = Focal length

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\\\Rightarrow \frac{1}{f}=\frac{1}{19.3}+\frac{1}{-52.3}\\\Rightarrow \frac{1}{f}=\frac{3300}{100939}\\\Rightarrow f=\frac{100939}{3300}=30.58\ cm$

The power of a lens is given by

$P=\frac{1}{f}\\\Rightarrow P=\frac{1}{0.358}=2.79\ D$

The power of her glasses should be 2.79 D