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{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} $