The resultant power of combination of lenses.

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Solution

The focal length of the combination of two lenses placed in contact is given by the relation.
$\frac{1}{F} = \frac{1}{f_{1}} + \frac{1}{f_{2}}$

If $p_{1}$ is the power of lens of focal length $f_{1}$ , $p_{2}$ the power of the focal length $f_{2}$ and $P$ the power of the combination of focal length, $F$ then,

$P = p_{1} + p_{2}$

Thus the power of the combination of lenses is the algebraic sum of the powers of individual lenses.
If two lenses are separated by a distance $d$ metre, then the power of the combination of lenses is given by a relation
$P = p_{1} + p_{2} - d \cdot (p_{1} \cdot p_{2})$

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