Question

A source of light is located at the double focal length distance from a convergent lens. The focal length of the lens is $f=30\text{cm}$. At what distance from the lens should a flat mirror be placed such that rays reflected from the mirror become parallel to the principle axis after passing through the lens for second time?

• A. $45\text{cm}$ from lens on opposite side of object.
• B. $30\text{cm}$ from lens on opposite side of object.
• C. $60\text{cm}$ from lens on opposite side of object.
• D. $25\text{cm}$ from lens on opposite side of object.

Answer 1

The correct option is A $45\text{cm}$ from lens on opposite side of object.


Object is at distance $2f$ from lens, thus after first refraction of rays from lens, image will form at $2f$ on opposite side.
$\Rightarrow O{O}^{\prime }=O^{\prime }{I}_1=2f=60\text{cm}$

For the ray's to become parallel after refraction from the lens second time, they must intersect at the focus of the lens after reflection from the mirror.
$\Rightarrow O^{\prime }{I}_2=f=30\text{cm}$

For plane mirrors, $M{I}_2=M{I}_1=\frac{60-30}{2}=15\text{cm}$

$\Rightarrow$ Distance of plane mirror from lens,
$O^{\prime }M=O^{\prime }{I}_2+M{I}_2$
$\therefore O^{\prime }M=30\text{cm}+15\text{cm}=45\text{cm}$

$\begin{array}{c}\text{Why this question?}\\ \text{It intends to challenge your application skill for}\\ \text{reflection from mirror and refraction from lens.}\end{array}$