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

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Answer 1

Let the two objects be $Q_{1} a n d Q_{2}$
For $Q_{1}$
$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$
Now, $v = - v$ and $u = - 20$
Putting back the values,
$\frac{- 1}{v} + \frac{1}{2 0} = \frac{1}{f}$
Similarly, for $O_{2}$ ,
$\frac{1}{v} + \frac{1}{4 0} = \frac{1}{f}$
Solving the 2 eqns simultaneously for f, we get f = $\frac{8 0}{3}$

Answer 2

Let the two objects be

Q_{1} a n d 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}{2 0} = \frac{1}{f}

Similarly, for

O_{2}

,

\frac{1}{v} + \frac{1}{4 0} = \frac{1}{f}

Solving the 2 eqns simultaneously for f, we get f =

\frac{8 0}{3}