An achromatic convergent lens of equivalent focal length +20 cm is made of two lenses (in contact) of materials having dispersive powers in the ratio of 1:2 and having focal lengths $f_{1}$ and $f_{2}$ . The correct option is

Question

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Answer 1

Using, the additive property of powers of a lens,
$P = P_{1} + P_{2}$

$\frac{1}{f} = \frac{1}{f _{1}} + \frac{1}{f _{2}}$

Also, the focal length is directly proportional to the dispersive power.

Hence, $\frac{f _{1}}{f _{2}} = - \frac{w _{1}}{w _{2}}$

Substituting the values as given in the question for $f = 20$ and the given ratio to be given as $1 : 2$ ,

We get, $f_{1} = 10$ and $f_{2} = - 20$

Answer 2

Using, the additive property of powers of a lens,

P = P_{1} + P_{2}

\frac{1}{f} = \frac{1}{f _{1}} + \frac{1}{f _{2}}

Also, the focal length is directly proportional to the dispersive power.

Hence,

\frac{f _{1}}{f _{2}} = - \frac{w _{1}}{w _{2}}

Substituting the values as given in the question for

f = 20

and the given ratio to be given as

1 : 2

,

We get,

f_{1} = 10

and

f_{2} = - 20