Biconvex lens kept on a plane mirror

Question

Q. A thin biconvex lens is kept on a plane mirror. When an object is kept at $20 cm$ in front of the lens, its image is formed at the same point. The focal length of the convex lens is
The solution given is
$frac{2}{20}=frac{1}{v}-frac{1}{u}$
and after putting the values we get $f=20cm $
My doubt is why that 2 above the 20 ??
As I am doing the solution I am getting answer as $f=10 cm$
And also according to the ray diagrams when you put an object on $-2f$ then it makes an invert image on $2f$. So according to that concepts the answers is $10cm$ where am I going wrong?
Or the answer given is wrong?

Bhavay · Accepted Answer

And also according to the ray diagrams when you put an object on −2f then it makes an invert image on 2f. So according to that concepts the answers is 10cm where am I going wrong?

This was true when there was no plane mirror kept behind the bi-convex lens.
The rays will become parellel after getting reflecting from plane mirror.
It will appear as rays are coming from infinity and now all the rays will get converge at focus of bi-convex lens.

My doubt is why that 2 above the 20 ??

I think the question can be treated as silvering of lens.
Silvering of Lens
In it the combined focal length of system becomes :$f_{lens}/2$ as $1/f_{mirror} =0$

trula · Answer

I do not know what u and v in your equation is, but if you consider the mirror and just construct the picture , the object and the picture must be at the focal distance. You do not have a real picture behind the mirror .
All the rays coming from the focal point are parallel after the lens and so are reflected to the focal point.

Biconvex lens kept on a plane mirror

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