A woman can read the large print in a newspaper only when it is at a distance of

Question

A woman can read the large print in a newspaper only when it is at a distance of 65 cm or more from her eyes. Is she nearsighted (myopic) or farsighted (hyperopic)? nearsighted farsighted What kind of lens is used in her glasses to correct her eyesight? converging lens converging lens diverging lens What should be the refractive power (in diopters) of her glasses (worn 1.7 cm from the eyes), so she can read the newspaper at a distance of 25 cm from the eyes? A person using a magnifying glass as in the figure observes that for clear vision its maximum angular magnification is 1.25 times as large as its minimum angular magnification. Assuming that the person has a near point located 22 cm from her eye, what is the focal length of the magnifying glass?

Explanation / Answer

Part-A : A woman can read the large print in a newspaper only when it is at a distance of 65 cm or more from her eyes.

(a) she is near-sighted (myopic).

(b) Converging lens is used in her glasses to correct her eye sight.

(c) using a len's formula, we have

1 / do + 1 / di = 1 / f

1 / [(25 - 1.7) cm] + 1 / -[(65 - 1.7) cm] = 1 / f

1 / f = 1 / (23.3 cm) + 1 / - (63.3 cm)

f = 36.8 cm

The refractive power (in diopters) of her glasses which is given as :

using a formula, we have

P = 1 / f (in meter) = 1 / (0.368 m)

P = 2.71 diopters

Part-B : Assuming that the person has a near point located 30 cm from her eye, then the focal length of magnifying glass will be given as -

For maximum angular magnification, we have

Mmax = (N / f) + 1                                                                     { eq.1 }

For minimum angular magnification, we have

Mmin = (N / f)                                                                           { eq.2 }

For a clear vision, its maximum angular magnification is 1.25 times as large as its minimum angular magnification.

Mmax = (1.25) Mmin

(N / f) + 1 = (1.25) (N / f)                                                      (from eq.1 & 2)

1 = [(1.25) - 1] (N / f)      

(0.25) (N / f) = 1

f = (0.25) N

where, N = near point distance = 22 cm

then, we get

f = (0.25) (22 cm)

f = 5.5 cm

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