Question

A convex lens of power $4\text{D}$ is placed at a distance of $40\text{cm}$ from a wall. At what distance from the lens should a candle be placed so that its image is formed on the wall?

• A. $\frac{100}{3}\text{cm}$
• B. $\frac{200}{3}\text{cm}$
• C. $\frac{500}{3}\text{cm}$
• D. $\frac{700}{3}\text{cm}$

Answer 1

The correct option is B $\frac{200}{3}\text{cm}$

Here,
$f=\frac{1}{P}=\frac{1}{4D}=\frac{1}{4}\text{m}=25\text{cm}$
Image has to be formed at the wall, hence image distance is, $v=+40\text{cm}.$
From Lens formula ,
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{u}=\frac{1}{v}-\frac{1}{f}$
$\Rightarrow \frac{1}{u}=\frac{1}{40\text{cm}}-\frac{1}{25\text{cm}}=-\frac{3}{200\text{cm}}$
$\text{Or},u=-\frac{200}{3}\text{cm}$
So, the candle should be placed at a distance $\frac{200}{3}\text{cm}$ from the lens on the opposite side of wall.