A stamp collector is viewing a stamp with a magnifying glass held next to her ey

Question

A stamp collector is viewing a stamp with a magnifying glass held next to her eye. Her near point is 22 cm from her eye.

A stamp collector is viewing a stamp with a magnifying glass held next to her eye. Her near point is 22 cm from her eye What is the refractive power of a magnifying glass that has an angular magnification of 6.32 when the image of the stamp is located at the near point? What is the angular magnification when the image of the stamp is 45 cm from the eye? I got the first part of the problem, but not the second part.

Explanation / Answer

Near point N = 22 cm = 0.22 m Angular magnification M = 6.32
(a)
from the given question with the image at the nearpoint of the eye the angular magnification will
be
M = (N / f) + 1
from which we get
(N / f) = M - 1
f = N / (M - 1)
= (0.22 m) / (6.32 - 1)
= 0.22/5.32 = 0.0413533
now the refractive power of the lens will be
RP = 1 / f
= 24.18 diopters
(b)
when the image of the stamp is 45 cm from the eye
M = [(1 / f) - (1 / di)] N
= [(1 / f) - (1 / -0.45m)] (0.22 m)
= [(1/24.18) + (1/0.45)](0.22 m) = [0.04136 +2.222](0.22 m) = 0.498 = 0.5    Near point N = 22 cm = 0.22 m Angular magnification M = 6.32
(a)
from the given question with the image at the nearpoint of the eye the angular magnification will
be
M = (N / f) + 1
from which we get
(N / f) = M - 1
f = N / (M - 1)
= (0.22 m) / (6.32 - 1)
= 0.22/5.32 = 0.0413533
now the refractive power of the lens will be
RP = 1 / f
= 24.18 diopters
(b)
when the image of the stamp is 45 cm from the eye
M = [(1 / f) - (1 / di)] N
= [(1 / f) - (1 / -0.45m)] (0.22 m)
= [(1/24.18) + (1/0.45)](0.22 m) = [0.04136 +2.222](0.22 m) = 0.498 = 0.5   

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