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Cutting of Thin Lenses

A combination...

Question

A combination of the two thin lenses of the same material with focal length, $f_{1}$ and $f_{2}$ are arranged on a common axis. In order to minimize the chromatic aberration, the distance between them should be :

\frac{(f_{1} + f_{2})}{4}

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\frac{(f_{1} + f_{2})}{2}

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(f_{1} + f_{2})

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2 (f_{1} + f_{2})

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Solution

The correct option is A $\frac{(f_{1} + f_{2})}{2}$
To minimize chromatic aberration the distance between two lenses is the average of there focal length. So, here given focal length are $f_{1} a n d f_{2}$ .
So, $f_{a v e r a g e} = \frac{f_{1} + f_{2}}{2}$ .

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If two thin lenses of focal length f₁ and f₂ are held in contact then the focal length of the combination will be

^{'} f^{'}

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\frac{1}{F} = \frac{1}{f_{1}} + \frac{1}{f_{2}} - \frac{d}{f_{1} f_{2}}

F =

f_{1}

f_{2}

^{'} d^{'}

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