Question

Two lenses of power $+10D$ and $-5D$ are placed in contact. Where should an object be held from the lens, so as to obtain a virtual image of magnification $2$?

• A. $5cm$
• B. $-5cm$
• C. $10cm$
• D. $-10cm$

Answer 1

Answer: (D)

$P_1=+10D,P_2=-5D$
$P=P_1+P_2=10-5=5D$
$f=\frac{100}{5}=20cm$
Magnification $=\frac{v}{u}=2$
$v=2u$
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$ (Lens formula)
$\Rightarrow \frac{1}{2u}-\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{-1}{2u}=\frac{1}{f}$
$\Rightarrow u=\frac{-f}{2}=\frac{-20}{2}=-10cm$