Concave and convex lenses are placed touching each other. The ratio of magnitudes of their focal lengths is 2:3. The focal length of the system is 30 cm. then the focal lengths of individual lenses are:

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-15, 10

75, 50

-75 ,50

75, -50

answer is B.

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Detailed Solution

$∵$ $f$ is +ve, $| P_{1} | > | P_{2} |$

$∴$ $\frac{f_{1}}{f_{2}} = \frac{- 2}{3} \Rightarrow f_{2} = \frac{- 3 f_{1}}{2}$

$\frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{f_{2}} \frac{1}{30} = \frac{1}{f_{1}} + \frac{1}{f_{2}} \frac{1}{30} = \frac{1}{f_{1}} + \frac{1}{\frac{- 3 f_{1}}{2}}$

$∴$ $f_{1} = 10 c m$ and $f_{2} = - 15 c m$ .

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