A point object is placed at a distance of `12 cm` from a convex lens of focal length `10 cm.` On the other side of the lens, a convex mirror is placed at a distance of `10 cm` from the lens such that the image formed by the combination coincides with the object itself. The focal length of the convex mirror is

Options

A. `25` cm
B. `50` cm
C. `10` cm
D. `20` cm

Answer

A

Explanation

For convex lens, `(1)/(v)-(1)/(-12)=(1)/(10)`
or, v= `60` cm
In the absensce of convex mirror lens will form the image `I_(1)` at a distance of `60` cm behind the lens. Since , the mirror is at a distance of `10` cm from the lens, `I_(1)` will be at a distance of `60-10=50` cm from the mirror, i.e., `MI_(1)=50` cm.

Now as the final image `I_(2)` is formed at the object O itself, the rays after reflection from the mirror retraces its path, i.e., rays on the mirror are incident normally, i.e., `I_(1)` is the center of the mirror, so that
`R=MI_(1)=50` cm
Hence, `f=((R)/(2))=((50)/(2))=25` cm