Magnification of a lens

Lenses give an image of the object. The size of the image compared with the object depends on the magnification of the lens.
The magnification of a lens is defined as:


In spite of what you might think magnifications don't always have to be bigger than one. For example in a camera and in your eyes the image is smaller than the object.


However if we look at the diagram and consider the triangles OO'P and II'P we can see that the magnification is also equal to image distance/object distance or v/u.
If the image is real and 7.5 cm from the lens and the object is real and 15 cm from the lens the magnification would be 7.5/15 or +0.5, the image is real and half the size of the object.

If the image is virtual and 24 cm from the lens and the object is real and 8 cm from the lens the magnification is -24/8 or -3, the image is virtual and three times the size of the object.