Question

How do you find the position and magnification of a convex mirror?

Answer 1

Hint: In this question we have to find the position and magnification of a convex mirror. The position means the position of the image of an object placed in front of the mirror or near the mirror. The magnification means what is the difference between the sizes of image of the object and the actual size of the object.

Complete answer:
As we know that the focal length of the mirror is denoted by f, the position of the object is denoted by u and the position of the image is denoted by v. The formula to find the focal length of the mirror is as follows;
\[\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}\]
From this formula we can find formula of position of image
\[\dfrac{1}{v} = \dfrac{1}{f} - \dfrac{1}{u}\]
Now, we are going to talk about magnification. Magnification is a measure of changes that we can see in the size of the object. It is defined as the negative of the ratio of the distance of the image to the distance of the object from the mirror. It is also defined as the height of the image to the height of the object. The formula of magnification is given below;
$m = - \dfrac{v}{u}$
Where, m is the magnification
u is the distance of object from the mirror
v is the distance of object from the mirror
f is the focal length of the mirror
Result- From above explanation we can clearly understand how we can find the position and magnification of a convex mirror.

Note: The way to find the position and magnification of a concave mirror is also the same as the above explanation and even for lenses also the explanation of the position and magnification will be the same. It is quite easy to find the position and magnification in a mirror but one thing that we have to be careful about is positive and negative signs of position of object and image. When the object is placed at the right side and the image is at right side then both will be positive. When the object is placed at the left side and the image is at the left side then both will be negative.