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  4. Two thin lenses have a combined power of +9 D. When they are separated by a distance of 20 cm, their equivalent power becomes +(27/5) D. Their individual powers (in diopters) are

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Q. Two thin lenses have a combined power of $+9 D$. When they are separated by a distance of $20\, cm$, their equivalent power becomes $ +\frac{27}{5} D$. Their individual powers (in diopters) are

KCETKCET 2011Ray Optics and Optical Instruments

Solution:

Given,
$P_{1}+P_{2}=9$
$P=P_{1}+P_{2}-d P_{1} P_{2}$
$\frac{27}{5}=9-\frac{20}{100} \times P_{1} P_{2}$
Hence, the above equation is correct for
$P_{1}=3$ and $P_{3}=6$