1. Use the lens relations

For a thin lens, taking magnitudes, $m=\frac{v}{u}$ and the lens formula is $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}.$

From magnification, $u=\frac{v}{m}.$ Substitute into the lens formula: $\frac{1}{f}=\frac{1}{v}+\frac{1}{v/m}=\frac{1}{v}+\frac{m}{v}=\frac{1+m}{v}.$ Hence, $m=\frac{v}{f}-1.$

So the graph of $m$ versus $v$ is a straight line with:

• slope $=\dfrac{1}{f}$
• intercept on the $m$-axis $=-1$

2. Read the slope from the graph form

Since the answer choices involve $a,b,c$, the graph must represent a straight line whose slope is given by $\text{slope}=\frac{c}{b}.$ Therefore, $\frac{1}{f}=\frac{c}{b}.$ So, $f=\frac{b}{c}.$

3. Match with the options

Thus the focal length is $\boxed{\frac{b}{c}}$ which corresponds to Option D.

4. Comparison with stored answer

Stored correct answer: D

My derived answer is also D.