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  4. Two thin lenses of focal lengths f1 and f2 are in contact and coaxial. The power of the combination is

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Q. Two thin lenses of focal lengths $f_{1}$ and $f_{2}$ are in contact and coaxial. The power of the combination is

Ray Optics and Optical Instruments

Solution:

If two thin lenses of focal lengths $f_{1}$ and $f_{2}$ are placed in contact coaxially, then equivalent focal length of combination is
$\frac{1}{F}=\frac{1}{f_{1}}+\frac{1}{f_{2}}-\frac{0}{f_{1} f_{2}}=\frac{1}{f_{1}}+\frac{1}{f_{2}}$
Power for the combination is
$P=\frac{1}{F}=\frac{1}{f_{1}}+\frac{1}{f_{2}}=\frac{f_{1}+f_{2}}{f_{1} f_{2}}$