Question

The following graph shows how the inverse of magnification $\frac{1}{m}$ produced by a thin convex lens varies with distance u. What is the focal length of lens used?

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

Answer 1

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

We know from lens formula
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
Multiplying both sides by $u$
$\frac{u}{v}-1=\frac{u}{f}$
Here $\frac{v}{u}=m$ so $\frac{u}{v}=\frac{1}{m}$
$\Rightarrow \frac{1}{m}-1=\frac{u}{f}$
$\Rightarrow \frac{1}{m}=\left(\frac{1}{f}\right)u+1$
Comparing with the straight line equation
$y=m^{\prime }x+c$
Where $m^{\prime }$ is the slope of the straight line
Here, we get that the slope is equal to $\frac{1}{f}$
and, Slope of given graph = $\frac{b}{c}$
$\Rightarrow \frac{1}{f}=\frac{b}{c}$
$\Rightarrow f=\frac{c}{b}$