Question

A point O is placed midway between the two converging mirror of focal length $f$ each. find $d$ so that object and image coincide :

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

Answer 1

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

We have, $u=-\frac{d}{2}$ ; $v=-\frac{d}{2}$ ; $f=-f$

From mirror formula, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\frac{-2}{d}-\frac{2}{d}=\frac{-1}{f}$

$d=4f$

Now if we assume $d=2f$ i.e, object is focus then ,rays after striking left mirror gets parallel to principal axis and strike right mirror which results in forming a image again at focus so $d=2f$ too satisfies the given conditions.

It can be solved alternatively by finding the image formed by left mirror which serves as object for right mirror and finding final image which results the same as above. Hence option $A$ is correct