Question

A concave lens produces an image 20 cm from the lens of an object placed 30 cm from the lens. The focal length of the lens is:
(a) 50 cm
(b) 40 cm
(c) 60 cm
(d) 30 cm

Answer 1

(c) 60 cm
Object distance from the lens, u = $-$30 cm
Image distance from the lens, v = $-$20 cm

Using the lens formula, we get:

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

$$\begin{gathered} \frac{\text{1}}{\text{f}}=\frac{\text{1}}{\text{-20}}-\frac{\text{1}}{\text{-30}} \\ \frac{\text{1}}{\text{f}}=\frac{\text{1}}{\text{-20}}+\frac{\text{1}}{\text{30}} \\ \frac{\text{1}}{\text{f}}=\frac{\text{-3+2}}{\text{60}}=-\frac{\text{1}}{\text{60}} \end{gathered}$$

∴ f = $-$60 cm

Therefore, the focal length of the lens is 60 cm.