34.5.3 Lateral Magnification

The image can be either larger or smaller than the object, depending on the location and focal length of the lens. But there’s more to a description of the image than just its size. We also want to know its orientation relative to the object. That is, is the image upright or inverted? It is customary to combine size and orientation information into a single number. The lateral magnification $m$ is defined as

m = - \frac{s'}{s}

(34.14)

You just saw in Example 34.7 that the image-to-object height ratio is $h' / h = s' / s$ . Consequently, we interpret the lateral magnification $m$ as follows:

A positive value of $m$ indicates that the image is upright relative to the object. A negative value of $m$ indicates that the image is inverted relative to the object.
The absolute value of $m$ gives the size ratio of the image and object: $h' / h = | m |$ . The heights $h$ and $h'$ are physical distances and are always positive numbers.

The lateral magnification in Example 34.7 would be $m = - 0.33$ , indicating that the image is inverted and 33% the size of the object.

NOTE The image-to-object height ratio is called lateral magnification to distinguish it from angular magnification, which we’ll introduce in the next chapter. In practice, $m$ is simply called “magnification” when there’s no chance of confusion. Although we usually think that “to magnify” means “to make larger,” in optics the absolute value of the magnification can be either $> 1$ (the image is larger than the object) or $< 1$ (the image is smaller than the object).