# How to find the focal distance of a Lens given its Magnification?

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.

• 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? – Cryo May 8 at 21:12
• 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 – user3347814 May 8 at 21:26
• 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? – user3347814 May 8 at 21:28
• 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. – Mark H May 8 at 21:37
• This should help: <en.wikipedia.org/wiki/Magnifying_glass#Magnification>. – Sebastian Riese May 8 at 22:05