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The dispersive power of the materials of the two lenses are in the ratio 4:3. If the achromatic combination of these two lenses in contact is a convex lens of focal length 60 cm, then the focal length of the component lenses are

A

20 cm and +25 cm

B

20 cm and -25 cm

C

15 cm and +20 cm

D

15 cm and -20 cm

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Solution

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Correct option is D)

For an achromatic combination,
$\frac{f _{1}}{w _{1}} + \frac{f _{2}}{w _{2}} = 0$

Also, the effective focal length of the combination will be:
$\frac{1}{f} = \frac{1}{f _{1}} + \frac{1}{f _{2}}$

Solving these simultaneously and substituting the values, the obtained focal lengths are, $f_{o} = 15$ and $f_{e} = - 20$

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