Question

The unit of magnification is:
A. $m$
B. ${{m}^{2}}$
C. ${{m}^{-1}}$
D. It is unitless

Answer 1

Hint: The magnitude of magnification produced by a mirror or lens is the ratio of the image height to the object height or equivalently the ratio of the image distance to the object distance. Therefore, it is the ratio of two quantities that have the same unit, that is, of length.

Complete step by step answer:
The image of an object, when produced by a mirror or lens is either enlarged, diminished or the same size as the object under suitable conditions. The magnitude of magnification produced by the lens or the mirror is defined as the ratio of the height of the image $\left( {{h}_{i}} \right)$ to the height of the object $\left( {{h}_{o}} \right)$ or equivalently, the ratio of the image distance $\left( v \right)$ to the object distance $\left( u \right)$.
Hence, the magnitude of magnification $\left| M \right|$ is given by,
$\left| M \right|=\dfrac{{{h}_{i}}}{{{h}_{o}}}=\dfrac{v}{u}$
Now, since, the ratio is of two quantities that have the same dimension (of length) and the same fundamental unit, therefore the ratio does not have any unit. The ratio of two similar quantities is unitless.
Therefore, going by this explanation, magnification produced by a mirror or lens is also unitless.
Hence, the correct option is D) it is unitless.

Note: Proper sign conventions must be used while writing the magnification for a mirror or lens, since the sign plays an important part in describing whether the image is virtual, real, inverted, etc. The magnitude only gives the extent of the difference between the image and object size, however, we can also know of their relative orientations by studying the sign of the magnification. For example, a negative magnification means that the image is inverted with respect to the object.