Question

The magnification for a mirror is $ - 3$. How are $u$ and $v$ related?

Answer 1

Hint We are given here with the magnification of a mirror and are asked to find a relation between the object distance and the image distance. Thus, we will use the formula of magnification in a mirror which relates the given parameters.
Formulae Used:
For any type of mirror,
$\Rightarrow$ $m = \dfrac{{ - v}}{u}$
Where, $m$ is the magnification of the mirror, $u$ is the object distance and $v$ is the image distance.

Complete Step By Step Solution
Here,
$\Rightarrow$ $m = - 3$
Thus, the image formed is a real and enlarged image.
Thus, the mirror is a concave mirror.
Now,
We know,
$\Rightarrow$ $m = \dfrac{{ - v}}{u}$
Putting in the value of$m = - 3$, we get
$\Rightarrow$ $ - 3 = \dfrac{{ - v}}{u}$
Further, we get
$\Rightarrow$ $v = 3u$
Hence, this is the required relation.

Additional Information There are basically two types of spherical mirrors. One is the type whose curving surface is the reflecting face. This mirror is named a convex mirror. Then, the second type whose incurving surface is the reflecting side. This mirror is named a concave mirror.
Now, there are few basic parameters we use while discussing any type of situation or problems for spherical mirrors.
First is the pole of the mirror. This is the geometrical center of the aperture of the mirror. It is denoted by the letter $P$.
Then comes the principal axis. It is the straight line passing through the pole.
Then comes the focus of the mirror. It is the point on the principal axis of the mirror at which the rays actually or seems to converge. It is denoted by the symbol $F$.
Then there is the center of curvature. It is the center of the sphere of which the mirror is a part of. It is denoted by the symbol $C$.


Note: Here, we found the mirror to be a concave one as the image formed was real in nature. But if the mirror was a convex one, then the magnification value would have been positive. But though, the formula of magnification remained the same.