Question

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

• A. 5 cm
• B. 10 cm
• C. 20 cm
• D. 50 cm

Answer 1

Answer: (C)

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,
$P_{eq}=P_1+P_2-2d{P}_1{P}_2$
$=10+10-2d(10\times 10)$
$=20-100d$
Now, $20-100d<0$
$\Rightarrow 100d<20$
$d>\frac{1}{5}m$
$\Rightarrow d>\frac{100}{5}cm$
or $20cm$