Question

A students plots a graph between inverse of magnification 1/$m$ produced by a convex thin lens and the object distance $u$ as shown in figure. What was the focal length of the lens used?

• A. $\frac{b}{ca}$
• B. $\frac{bc}{a}$
• C. $\frac{c}{b}$
• D. $\frac{b}{c}$

Answer 1

Answer: (C)

$\frac{c}{b}$

Answer 2

Lens formula,$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
or $\frac{u}{v}-1=\frac{u}{f}$
$\Rightarrow \frac{1}{m}-1=\frac{u}{f}$
or $\frac{1}{m}\left(\frac{1}{f}\right)u+1$
this is the equation of a straight line whose slope
$\frac{1}{f}=\frac{b}{c}$
$\therefore f = \frac{c}{b}$