Question

The distance between an object and the screen is $100cm$. A lens produces an image on the screen when the lens is placed at either of the positions $40cm$ apart. The power of the lens is nearly

• A. $5diopter$
• B. $2diopter$
• C. $9diopter$
• D. $3diopter$

Answer 1

Answer: (A)

At first position of lens, let the distance of lens from object and screen be $x$ and $y$, respectively.
$\therefore x+y=100....\left(i\right)$
$\therefore$ At second position of lens, the distance of lens from object and screen shall be $y$ and $x$, respectively.
$\therefore y-x=40....\left(ii\right)$
Solving Eqs. (i) and (ii), we get
$y=70cm=\frac{70}{100}m$ and $x=30cm=\frac{30}{100}m$
Therefore, the power of lens is
$\frac{1}{f}=\frac{1}{y}+\frac{1}{x}=\frac{100}{70}+\left(\frac{100}{30}\right)=\frac{100}{21}\approx 5diopter$.