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

Question

Aicharya · Accepted Answer

The correct option is (D). Given, combined power of the lenses: $P_1+P_2=9 \quad \ldots (1)$
If a separation $d$ is added between the lenses, then
$\begin{aligned}
& P=P_1+P_2-d_1 P_2 \\
& \left(\frac{27}{5}\right)=9-0.20 \times P_1 P_2 \\
& P_1 P_2=18 \quad \ldots (2)
\end{aligned}$ On solving equation (1) and (2), $P_1=3 D$ and $P_2=6 D$

Two thin lenses have a combined power of $+9 D$. When they are separated by a distance of $20 \mathrm{~cm}$,…

Solution