Magnification

It is natural to define the magnification created by a lens as the ratio of the height of the image to the height of the object. In Figure (2) we have reproduced Figure (1) emphasizing the heights of the objects and images. We see that the shaded triangles are similar, thus the ratio of the height B of the first image to the height A of the object is

Figure 1: Locating the image in a two lens system.

We could define the magnification in the first lens as the ratio of B/A, but instead we will be a bit tricky and include a - (minus) sign to represent the fact that the image is inverted. With this convention we get

Treating B as the object for the second lens gives

The total magnification m₁₂ in going from the object A to the final image C is

which has a + sign because the final image C is upright. But

Thus we find that the final magnification is the product of the magnifications of each lens.

Figure 2: Magnification of two lenses.