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

- 50 c m, + 100 c m

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+ 50 c m, - 100 c m

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- 50 c m, - 100 c m

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+ 50 c m, + 100 c m

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Solution

The correct option is B $+ 50 c m, - 100 c m$
$f = 100 c m$ , Now, from question: $f_{1} : f_{2} = 1 : 2 ⟹ f_{2} = 2 f_{1}$
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: $f_{o} = 50 a n d f_{e} = - 100$

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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:

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