Question

Two point objects are placed on principal axis of a thin converging lens. One is 20 cm from the lens and other is on the other side of lens at a distance of 40 cm from the lens. The images of both objects coincide. The magnitude of focal length of lens is

• A. $\frac{80}{3}cm$
• B. $\frac{40}{3}cm$
• C. $40cm$
• D. $\frac{20}{3}cm$

Answer 1

Answer: (A)

$\frac{80}{3}cm$

Let the two objects be $Q_{1}and{Q}_2$
For $Q_1$
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
Now, $v=-v$ and $u=-20$
Putting back the values,
$\frac{-1}{v}+\frac{1}{20}=\frac{1}{f}$
Similarly, for $O_2$,
$\frac{1}{v}+\frac{1}{40}=\frac{1}{f}$
Solving the 2 eqns simultaneously for f, we get f = $\frac{80}{3}$