Question

A woman can read the large print in a newspaper only when it is at a distance of 61 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 2.3 cm from the eyes), so she can read the newspaper at a distance of 24 cm from the eyes?

Answer 1

a) far sighted (convex lens)

b) 0.00477D

Step-by-step explanation:

a) She is far sighted. Far sightedness also known as hypermetropia is an eye defect in which an individual can see only far distant object but not close ranged object. Since the woman can see at a distance of 61cm from her eye then she is far sighted. A short sighted person can only see an object close at a maximum distance of 25cm from the eye.

Long sight can be corrected using a convex lens. This lens will converge all rays and focus them on the retina.

b) Refractive power is the power of the lens and is defined as the reciprocal of the focal length.

P = 1/f

Using the lens formula

1/f = 1/u+1/v where:

f is the focal length

u is the object distance

v is the image distance

Given u = 24cm, v = 2.3cm

1/f = 1/24+1/2.3

Note that the image distance is taken as positive for convex lens.

1/f = 0.0417+0.435

1/f = 0.4767cm

Power of the lens in diopter = 0.00477D (This is gotten by converting the answer gotten to metres)