Question

A point object O is placed at a distance o 20cm from a convex lens of focal 10 cm as shown. At what distance x from lens should a concave mirror of focal length 60 cm can be placed so that final image coincides with object.; (a)20cm(b)30cm(c)40cm(d)50cm

Answer 1

Focal Length of convex lens = 10cm.
 So, radius of curvature = 20 cm.

Clearly, object is placed at the radius of curvature.
∴ Image is formed at the radius of curvature.

Now, focal length of concave mirror = -60 cm.
Image distance = -20 cm.
 x = ?

Using mirror formula,
$\frac{-1}{60} + \frac{1}{20}= \frac{1}{x}$
Or, 
$\frac{2}{60} = \frac{1}{x}$

Hence, x = 30 cm.

I think this is the answer. Honestly, I ain't sure.
Hope it helped!
NISHTHA.

Answer 2

Answer: 20cm

Explanation: since object is at 20cm = 2f, therefore it’s image will be formed at 20cm on the other side of lens. So, if the mirror is placed at 20cm, then rays from the image will fall on the pole of the mirror symmetrically and so it can retrace it’s path and the final image will be at the position of object.