Question

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

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

Answer 1

Answer: (D)

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