A stamp collector is viewing a stamp with a magnifying glassheld next to her eye

Question

A stamp collector is viewing a stamp with a magnifying glassheld next to her eye. Her near point is 25 cm from her eye.(a) What is the refractive power of a magnifyingglass that has an angular magnification of 4.7 when the image ofthe stamp is located at the near point? (b) Whatis the angular magnification when the image of the stamp is 54 cmfrom the eye?
I figured out (a), which is 14.8 diopters. I can't figure out(b) though, I've tried it 3 times...I have gotten answers of 5.46,4.163, and 3.237. Any help would be much appreciated. A stamp collector is viewing a stamp with a magnifying glassheld next to her eye. Her near point is 25 cm from her eye.(a) What is the refractive power of a magnifyingglass that has an angular magnification of 4.7 when the image ofthe stamp is located at the near point? (b) Whatis the angular magnification when the image of the stamp is 54 cmfrom the eye?
I figured out (a), which is 14.8 diopters. I can't figure out(b) though, I've tried it 3 times...I have gotten answers of 5.46,4.163, and 3.237. Any help would be much appreciated.

Explanation / Answer

We are given that
Near point,N = 25 cm and Angular magnification,M = 6.9

(a) Focal length f can be foundusing, f = N/(M-1) = (25cm)/(4.7-1) = 25cm / 3.7 = 6.76 cm= 0.0676 m (b)When the image of the stamp is 54 cm from the eye, M = (1/f - 1/di)N      = [1/6.76 - 1/(-54)]( 25)      = 4.161 Solve it I hope it helps you

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