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Power and Thin Lenses in Contact

Two convex le...

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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