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. $-5$
• C. $10cm$
• D. $-10cm$

Answer 1

Answer: (D)

Here, $P_1=+10D,P_2=-5D$
Combined power,
$P=P_1+P_2=10D-5D$
$P=5D$
$\therefore$ Combined focal length
$=\frac{1}{P}m=\frac{100}{P}cm=\frac{100}{5}=20cm$
Given magnification,
$m=2$
$\frac{v}{u}=2$
$v=2u$
By lens formula,
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\frac{1}{2u}-\frac{1}{u}=\frac{1}{20}$
$\frac{1-2}{2u}=\frac{1}{20}$
$2u=20$
$u=-10cm$
Hence, to obtain virtual image, object should be place at a distance of 10 cm