# When given magnification alone,for an upright, virtual image, with convex lens, how can I find object distance [closed]

Formula involved in such calculations, similar examples, link associated with d question

• Have you done any of your own research? There are many sites on line with equations. – Bill N May 3 at 13:22

With magnification alone? Impossible. You need to know at least something more. Here's, for example, if you also know focal length.

First, one of the standard formulas for magnification is: $$m=-\frac{s_i}{s_o}$$. Using that and the usual $$\frac{1}{f}=\frac{1}{s_i}+\frac{1}{s_o}$$:

$$\frac{1}{f}=\frac{1}{s_o}-\frac{1}{m s_o}$$

$$s_o = f \left( 1 - \frac{1}{m} \right)$$

For an upright image, $$m$$ is positive. For convex lens, $$f$$ is positive. For an object in front of the lens, $$s_o$$ is positive and for the image behind the lens, $$s_i$$ is positive.

For a real image, image and object are on the opposite sides so $$s_o$$ and $$s_i$$ are either both positive or both negative. For a virtual image, they are on the same side so they have opposite signs.

• Shouldn't your very first equation have the ratio of image distance to object distance? – Not_Einstein May 3 at 13:23
• @not Yeah, I caught that. Was too quick to post. -.- – relatively_random May 3 at 13:25