Question

Magnification \[(m) = ?\]
A. \[\dfrac{v}{u}\]
B. \[\dfrac{u}{v}\]
C. \[\dfrac{{{h_o}}}{{{h_i}}}\]
D. \[\dfrac{{{h_i}}}{{{h_o}}}\]

Answer 1

Hint: We are asked to find the correct formula for magnification from the following four options. We start by thinking of a logical explanation for magnification. Then we can move onto finding the physical definition of magnification and thus leading us to the right answer.

Formulas used:
The formula to find the magnification of a given object and image is given as,
\[m = - \dfrac{v}{u}\]
\[\Rightarrow m = \dfrac{{{h_i}}}{{{h_o}}}\]
Where \[v\] is the distance from the mirror or lens to the image, \[u\] is the distance from the mirror or lens to the object, \[{h_i}\] is the height or the size of the image and \[{h_o}\] is the height or size of the object.

Complete step by step answer:
We are asked to pick an option that is apt for defining magnification. The first thing that pops into our mind when we hear the word “magnification” is the measure of how big something is. In optics, the definition is very similar to this. Magnification is defined as the unitless quantity that measures how big or small (how much change in size) the object has become.

To be more precise it can be defined as the negative ratio of the distance from the mirror or lens to the image to the distance from the mirror or lens to the object. There is one more definition for magnification, it can also be defined as the ratio of the size or height of the image to that of the object.

Therefore, the right answer is option (D).

Note: The magnification with respect to the image and object distance is taken as a negative value because real images are formed in the backside of the mirror or lens.Magnification is the enlargement of the apparent size and not the physical size.