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  4. Two lenses have 10 D power each and they are separated by a distance. Beyond which distance does the power of combination changes from positive to negative?

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Q. Two lenses have $ 10\, D $ power each and they are separated by a distance. Beyond which distance does the power of combination changes from positive to negative?

AMUAMU 2016Ray Optics and Optical Instruments

Solution:

Let the power of lenses are $P_1$ and $P_2$ respectively. When they are separated by distance $d$, the equivalent power of the combination,
$P_{eq} = P_1 + P_2 - 2dP_1P_2$
$ = 10 + 10 - 2d (10\times 10)$
$ = 20 - 100\,d$
Now, $ 20 - 100 d < 0$
$\Rightarrow 100d < 20$
$ d > \frac{1}{5} m$
$ \Rightarrow d > \frac{100}{5} cm$
or $ 20\,cm$