The graph shows how the magnification m produced by a thin lens varies with image distance v. The focal length of the lens used is

 Step 1: Lens formula and magnification

$$\ \frac{\ 1}{v}-\ \frac{\ 1}{u}=\ \frac{\ 1}{f}$$

Magnification:

$$\ m=\ \frac{\ v}{u}$$

From lens relations:

$$\ m=\ \ 1\ -\ \ \frac{\ v}{f}$$

 Step 2: At v=a

$$\ m_1=\ \ 1\ -\ \ \frac{\ a}{f}$$

 Step 3: At v=a+b

$$\ m_1=\ \ 1\ -\ \ \frac{\ a\ +\ b}{f}$$

 Step 4: Subtract equations

Let:

$$c\ =\ m_{2\ }-m_1$$

$$c\ =\ \frac{\ a}{f}\ \ -\ \frac{\ a\ +\ b}{f}\ \ $$

$$c=\frac{a}{f}-\frac{a+b}{f}$$​

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

 Step 5: Simplify 

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