Question

A plane mirror and concave mirror are $50cm$ apart. An object is $30cm$ from a concave mirror such that image of the two coincide. The focal length of the concave mirror is

• A. $21cm$
• B. $18cm$
• C. $15cm$
• D. none of the above

Answer 1

The correct option is A $21cm$

Distance of object from the plane mirror is, $50cm-30cm=20cm$. So distance of image in plane mirror from the concave mirror is $50cm+20cm=70cm$.

Let the focal length of concave mirror be $f$.

From the mirror equation, $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}=\frac{1}{-30}+\frac{1}{-70}=-\frac{1}{21}$.

$f=-21cm$

So the focal length is $21cm$.