Question

Which one of the following is the correct expression for linear magnification for lens.

• A. $\frac{f}{f-u}$
• B. $\frac{-f}{f+u}$
• C. $\frac{f}{f+u}$
• D. $\frac{u+f}{f}$

Answer 1

The correct option is C

$\frac{f}{f+u}$

We know that,

$m=\frac{v}{u}$ ----- (i)

and $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$ (lens formula)

Or, $\frac{1}{v}=\frac{1}{u}+\frac{1}{f}$

Or, $\frac{1}{v}=\frac{u+f}{uf}$

Or, $v=\frac{uf}{u+f}$ --------- (ii)

Put the value of v in equation (i)

$m=\frac{\text{/}uf}{(u+f)\text{/}u}=\frac{f}{f+u}$

Hence, $m=\frac{f}{f+u}$