Question

A converging lens and a diverging mirror are placed at a separation of $20\text{cm}$. The focal length of the lens is $30\text{cm}$ and that of the mirror is $50\text{cm}$ . Where should a point source be placed between the lens and the mirror so that the light, after getting reflected by the mirror and then getting transmitted by the lens, comes out parallel to the principal axis?

• A. $17.5\text{cm}$ from lens
• B. $2.5\text{cm}$ from lens
• C. $10\text{cm}$ from mirror
• D. $19.5\text{cm}$ from lens

Answer 1

The correct option is A $17.5\text{cm}$ from lens

Let the point source be placed at distance $x$ from the mirror.


For the light to travel parallel to the principal axis, the source must be placed at focal point.

From the diagram we can deduce that,

For a diverging mirror,

$u=-x\text{cm},v=10\text{cm}$ and $f=50\text{cm}$

$\therefore$ Using , $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$

$\frac{1}{+50}=\frac{1}{-x}+\frac{1}{+10}$

$\Rightarrow x=\frac{10}{4}\text{cm}\text{or}2.5\text{cm}$ (from mirror)

$\therefore$ position of point object from lens $=20-2.5=17.5\text{cm}$

Hence, option (a) is the correct answer.