Question

The graph shows the variation of magnification $\left(m\right)$ produced by a convex lens with the image distance $\left(v\right)$. The focal length of the lens is

• A. $\frac{b}{c}$
• B. $\frac{c}{b}$
• C. $b$
• D. $\frac{ab}{c}$

Answer 1

Answer: (B)

$\frac{c}{b}$

$m=\frac{v}{u}$
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
Multiply the equation by v
$1-\frac{v}{u}=\frac{v}{f}\Rightarrow \frac{v}{u}=1-\frac{v}{f}$
$\therefore m=1-\frac{v}{f}$
Slope $=-\frac{1}{f}=\frac{b}{c}\Rightarrow f=\frac{c}{b}$