A peson looks into a spherical mirror. The size of image of his face is twice the actual size of his face. If the face is at a distance of 20cm, then find the radius of curvature of the mirror.

Explanation

Person will see his face only when the image is virtual Virtual image of real object is erect Hence `m = 2`
`:. (-v)/(u) = 2 rArr v = 40cm`
Applying `(1)/(v) + (1)/(u) = (1)/(f) , f = -40cm` or `R = -80cm` (concave) `:. R.O.C = 80cm`
Alter: `m = (f)/(f-u) rArr 2 = (f)/(f-(-20))`
`rArr f = -40cm` or `R = -80cm` (concave) `:. R.O.C = 80cm`