The single, thin lens and the formulas that describe it are some of the most basic elements of optics. When combined with the mathematics of more complex types or systems of lenses and mirrors, it is possible to determine the characteristics of almost any optical system from only a few parameters. However, many questions are more simply answered. One characteristic easy to determine—often important in basic optics and of unquestionable practical importance—is the magnification of a single lens system.

Determine the focal distance of the lens for which you are trying to find the magnification. With a real lens, do this by measuring the distance between the central plane of the lens and the point at which parallel rays of light (like those of the sun) passing through the lens are focused to a point. For a theoretical lens, one way to determine the focal distance is as follows: Take the inverse of the sum of the inverses of the distances from the object being magnified to the lens and from the image to the lens.

Calculate the magnification of the lens by dividing the focal distance by the focal distance minus the distance between the object and lens (M = f/[f-d]). This will yield a negative answer for magnification if the image is real and inverted (as in the case of convex lenses) and a positive answer if the image is virtual (on the same side of the lens as the object) and right-side up (as for concave lenses).

## Sciencing Video Vault

Apply the following if the focal distance is difficult to determine or if you know the distance between the object and lens as well as that between the image and the lens. In this case, the magnification may be determined by simply dividing the image distance by the object distance.