Question

The disatnce between an object and a screen is $100\text{cm}$. A lens produces an image on the screen when placed at either of the two positions $40\text{cm}$ apart. The power of the lens is nearly

• A. $3\text{D}$
• B. $5\text{D}$
• C. $7\text{D}$
• D. $9\text{D}$

Answer 1

The correct option is B $5\text{D}$

At first position of lens,
Let distance of lens from object and screen be $x$ and $y$ respectively
$\Rightarrow x+y=100\dots \left(1\right)$

At second position of lens, the distance of lens from object and screen shall be $y$ and $x$ respectively.
$y-x=40\text{cm}\dots \left(2\right)$
By solving $\left(1\right)$ and $\left(2\right)$ we get
$y=70\text{cm},x=30\text{cm}$
Therfore power of lens
$P=\frac{1}{f}=\frac{1}{v}-\frac{1}{u}=\frac{1}{y}+\frac{1}{x}$
$P=\frac{100}{70}+\frac{100}{30}=\frac{100}{21}\approx 5\text{D}$