A beam of light converges to a point on a screen S. A mirror is placed in front of the screen at a distance of 10cm form the screen. It is found that the beam now converges at a point 20cm in front of the mirror. Find the focal length of the mirror.

Explanation

The mirror can be concave or convex. Let f be the focal length. Let the incident rays be directed toward right as shown. All quantities toward right will be postive.
The initial point of convergence `(O)` now acts as a virtual object for the mirror.
Hence, `u=-10cm ` and `v=-20cm`
`f=(uv)/(u+v)=(-200)/(10-20)=+20cm`
As the focal length is positive, the mirror is convex having focal length 20cm.