Question

A point object $S$ is placed midway between two concave mirrors having equal focal length $f$ as shown in the figure. Find the possible value(s) of $d$ for which only one image is formed of the object.

• A. $d=2f,4f$
• B. $d=2f,3f$
• C. $d=3f,4f$
• D. $d=2f$

Answer 1

The correct option is A $d=2f,4f$

Given that both the mirrors have equal focal length $f$.
They will produce one image under two conditions.
Case I : When the object is at distance $f$ from each mirror. The rays from the object after reflecting from one mirror will become parallel to the other mirror and so these parallel rays after the reflection from the other mirror will converge on the object itself. So, only one image is formed. Here, $d=f+f=2f$.


Case II : When the object is at distance $2f$ from each mirror i.e. the object is at the centre of curvature of the mirrors, then the image will be produced at the same point $S$. So, only one image is formed. Here, $d=2f+2f=4f$