Question

Write the significance of the positive sign of the magnification.

Answer 1

Hint: In order to find the significance of positive sign of magnification, we could recall the definitions of magnification as a first step. From the two definitions of magnification, you could understand the meaning of positive sign of magnification. Hence, you can understand its significance.

Complete answer:
In the question, we are asked to find the significance of the positive sign of the magnification. In order to answer that let us recall the definition of magnification.
We know that magnification of a mirror can be given by two expressions: one in terms of height of image $\left(h_i\right)$ and object $\left(h_o\right)$ and the other in terms of object distance (u) and image distance (v).
Magnification can be defined as the ratio of image distance to the object distance, that is,
$m=-{\displaystyle \frac{v}{u}}$
Magnification can also be defined as the ratio of image height to the object height, that is,
$m={\displaystyle \frac{h_i}{h_o}}$
By convention the measurement taken to the right of the pole is taken positive and to the left is taken negative, as the object is always kept in front of the mirror, it will always be negative. So, by the first definition of magnification, we find that when the magnification is positive, it would mean that the image is formed behind the mirror and we call such images virtual. So, positive magnification would mean that the image formed is virtual.
Also, by convention, the measurements taken above and below the optic axis are considered positive and negative respectively. So when the magnification is positive it would mean that the image formed is erect.
Hence, we found the significance of positive sign of magnification to be the ability to find the nature of the image as erect and virtual.
Let us depict such a condition in a diagram for an object kept between C and F in front of a convex mirror,

Here, though the image formed is diminished, the magnification will be positive as the image formed is erect and virtual.

Note:
When we say power of magnification in optics, you shouldn’t confuse it with the optical power which is an entirely different concept. Power of magnification is actually the ratio of apparent size of an object to that of its true size or the ratio of image distance to the object distance. That is, it is a dimensionless number. Also, magnifying an object cannot change the perspective of the image.