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An achromatic doublet is a converging lens of equivalent focal length 100cm. If the dispersive powers of the material of the lenses are in the ratio 1:2. The focal lengths of the two lenses are:

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f=100cm, Now, from question: f1:f2=1:2⟹f2=2f1

For an achromatic combination, f1w1+f2w2=0

Also, the effective focal length of the combination will be,

1f=1f1+1f2

Solving these simultaneously and substituting the values,

the obtained focal lengths are: fo=50 and fe=−100

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