Question

Magnification produced by a rear view mirror fitted in vehicles is?

Answer 1

Step 1: Magnification

1. Magnification produced by a lens is defined as the ratio of the size of the image formed by the lens to the size of the object.
2. If the size of the image formed by the lens is $h_2$ and the original size of the image is $h_1$ then the magnification is given as,

$m=\frac{h_2}{h_1}$

Step 2: Magnification of Convex Mirror

Convex mirrors are fitted in a rearview mirror.

The figure shows the formation of image $A\text{'}B\text{'}$ a finite object $AB$ by a convex mirror.

Now, $△APB$ is similar to $∆A\text{'}PB\text{'}$

$\therefore \frac{A\text{'}B\text{'}}{AB}=\frac{PB\text{'}}{PB}$

Upon applying the sign convention we get,

$A\text{'}B\text{'}=+h_2$ (Downward image height)

$AB=+h_1$ (Upward object height)

$PB=-u$ (Object distance on left)

$PB\text{'}=+v$ (Image distance on left)

$\therefore \frac{+h_2}{+h_1}=\frac{+v}{-u}$

$\therefore$Magnification, $m=\frac{h_2}{h_1}=-\frac{v}{u}$

The smaller value of magnification occurs for diminished images because the size of the image is less than the size of the object.

Hence, the magnification is negative for convex mirrors.