An object is placed 60 cm away from a convex mirror. The size of the image is `(1)/(3)rd` the size of the object. Determine the radius of curvature of the mirror.

Explanation

We have from the mirror equation,
`f=(uv)/(u+v)`
Since, the image of a real object formed by a convex mirror is virtual therefore, v is positive but u is negatiev [Fig.1.38.]
According to the question,
`m=|v|/|u|=+(1)/(3)`
`or, " "v=|u|/|3|=|60|/|3| [therefore u=60cm]`
`or, " " v=20 cm`
Now, substituting the of fu and v with their proper sign in equation `(1)` we get,
`f=(-60xx(+20))/(-60+20)=30cm`
`therefore` The radius of curvanture of the spherical mirror,
`r=2f=2xx(+30)=60 cm`