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I came across this problem in my physics class, but I don´t how to solve it. The problem is:

A magnifying glass is used to produce a 4x magnification image. What is the focal distance of its lens?

I know the answer is $+6,25\,$cm, but I don´t know how to solve it.

I´ve tried using the lens formula $\,1/f = 1/d + 1/d_0\ $ and combining it with the magnification formula $M = -d_0/d$, but it did not work.

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    $\begingroup$ You are missing some piece of information here. Magnification tells you by how much things change, but you still need a value that will be changing. You need a distance of some sort. Draw a diagram. object --- Lens --- eye. What are the distances between these three objects? $\endgroup$ – Cryo May 8 at 21:12
  • $\begingroup$ This is also my conclusion. But the exercise does not give me any other information. It is a multiple choice question. Could you answer this question given the following alternatives? a) -6.25 cm, b)+4 cm, c) -4 cm, d)+6.25cm $\endgroup$ – user3347814 May 8 at 21:26
  • $\begingroup$ I know the focus point must be positive, for a diverging lens would not produce magnification. But is there a way to exclude the +4 cm answer? $\endgroup$ – user3347814 May 8 at 21:28
  • $\begingroup$ No. As long as the object's distance is 3/4 the focal length, you will get a magnification of 4x. So, 3cm from the 4cm lens and 4.7cm from the 6.25cm lens will both produce the same magnification. $\endgroup$ – Mark H May 8 at 21:37
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    $\begingroup$ This should help: <en.wikipedia.org/wiki/Magnifying_glass#Magnification>. $\endgroup$ – Sebastian Riese May 8 at 22:05

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