Question

The distance between an object and a divergent lens is m times the foal length of the lens. the linear magnification produced by the lens is

• A. m
• B. 1/m
• C. (m+1)
• D. $\frac{1}{m+1}$

Answer 1

The correct option is D $\frac{1}{m+1}$

It is given that $u=-mf$

Applying the lens formula

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\frac{1}{v}-\frac{1}{-mf}=\frac{1}{-f}$

$\frac{1}{v}=\frac{1}{-f}-\frac{1}{mf}$

$\frac{1}{v}=\frac{-1}{f}\left(1+\frac{1}{m}\right)=\frac{-1}{f}\left(\frac{m+1}{m}\right)$

$\therefore v=\frac{-fm}{m+1}$

$m=\frac{v}{u}=\frac{-fm}{m+1}\times \frac{1}{-mf}=\frac{1}{m+1}$

Hence the correct answer is option (D).