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A convex lens form a real image of a point object at a distance of 50cm from the convex lens is placed 10cm behind the convex lens on the image side .On placing a plane mirror on the image side and facing the concave lens ,it is observed that the final Image now coincides with the object itself .The focal length of the concave lens is

1)50cm 2)20cm 3)40cm 4)25cm

Dear student, you question is incomplete. However, I am trying to solve your problem.

From the last part of your question which says image coincides with the object. It means light rays retraces its path. So the rays are falling perpendicular to the plane mirror. This means that the images is formed at infinity by the concave lens.

The image for the first lens will be the virtual object for the second lens.

So, for concave lens,

Using the lens formula we haveThe image for the first lens will be the virtual object for the second lens.

So, for concave lens,

*u*= + 40 cm*v*= ∞$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{1}{f}=\frac{1}{-\infty}-\frac{1}{40}\phantom{\rule{0ex}{0ex}}\Rightarrow f=-40\mathrm{cm}$

Thus, the focal length of concave mirror is 40 cm.

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