Question

An object is placed at a distance of $15$ cm from a convex lens of focal length $10$ cm. On the other side of the lens, a convex mirror is placed such that its distance from the lens equals focal length of the lens. The focal length of the convex mirror is

• A. 20 cm
• B. 10 cm
• C. 15 cm
• D. 30 cm

Answer 1

The correct option is B 10 cm

Here point I would be center of curvature of the mirror.

So focal length of mirror $f=\frac{MI}{2}$

For lens, $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

$\frac{1}{v}=\frac{1}{f}+\frac{1}{u}$

Here , $f=+10cm,u=-15cm$

$\frac{1}{v}=\frac{1}{10}+\frac{1}{-15}$

$v=+30cm$

$MI=LI-LM$

$=30-10=20cm$

$f=\frac{MI}{2}=\frac{20}{2}$

$f=10cm$