Question

Magnification produced by a convex mirror is always:

• A. Equal to $1$
• B. Less than $1$
• C. More than $1$
• D. Zero

Answer 1

The correct option is B

Less than $1$

Magnification

1. Magnification produced by a lens is defined as the ratio pf 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,

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

Magnification of convex mirror

The figure shows the formation of image $A\text{'}B\text{'}$of 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, $m=\frac{h_2}{h_1}=-\frac{v}{u}$

Therefore, the magnification is negative, i.e., less than $1$ for convex mirrors.

As the size of the image is less than the size of the object, thus, the value of the magnification is smaller than one.

Hence, the correct answer is option (B).