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Power and Thin Lenses in Contact

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Question

Two convex lenses of focal lengths 10 cm and 20 cm are kept apart. If the resultant focal length of such combination is 8 cm, the distance between the lenses is:

A

10 cm

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B

5 cm

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C

20 cm

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D

15 cm

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Solution

The correct option is B 5 cm
Equivalent focal length, $f_{e q} = \frac{f_{1} f_{2}}{f_{1} + f_{2} - d}$

$8 = \frac{10 \times 20}{30 - d}$

$240 - 8 d = 200$

$\frac{40}{8} = d$

Distance between lenses, $d = 5 c m$

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