Question

The graph shows how the magnification $m$ produced by a thin lens varies with image distance $v$. What is the focal length of the lens used ?

• A. $\frac{b^2 c}{a}$
• B. $\frac{b^2}{ac}$
• C. $\frac{a}{c}$
• D. $\frac{b}{c}$

Answer 1

Answer: (D)

$\frac{b}{c}$

Answer 2

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ $1- \frac{v}{u} = \frac{v}{f}$ $1-m = \frac{v}{f}$ $m = 1 - \frac{v}{f}$ At $v =a , m_{1} =1 - \frac{a}{f}$ At $v = a +b, m_{2} = 1 - \frac{a+b}{f}$ $m_{2} -m_{1} =c = \left[1- \frac{a+b}{f}\right] - \left[1- \frac{a}{f}\right]$ $c = \frac{b}{f}$ $f= \frac{b}{c}$