Question

A point object $O$ is placed at a distance of $20cm$ from a convex lens of focal length $10cm$ as shown in fig. At what distance $x$ from the lens should a concave mirror of focal length $60cm$, be placed so that the final image coincides with the object?

Answer 1

Given that,

Focal Length of convex lens$f=10cm$

So, radius of curvature$r=20cm$

We know that, the object is placed at the radius of curvature

So, the image is formed at the radius of curvature

Now,

The focal length of concave mirror$f=-60cm$

Image distance$v=-20cm$

Now, using mirror formula

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

$\frac{-1}{60}+\frac{1}{20}=\frac{1}{x}$

$x=30cm$

Hence, the distance is $30cm$