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

The correct option is C $\frac{c}{b}$

Given,

Slope of the curve $=\frac{b}{c}$

Lens formula, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$--------(1)

Multiply by $u$ in both side in equation (1)

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

$\frac{1}{f}=\frac{b}{c}$

$\therefore f=\frac{c}{b}$