An object is placed beyond the center of curvature $C$ of the given concave mirror. If the distance of the object is $d_1$ from $C$ and the distance of the image formed is $d_2$ from $C$, the radius of curvature of this mirror is :

The correct option is D $\frac{2d_1{d}_2}{d_1-d_2}$
Since, the object lies beyond the center of curvature of the mirror, the image will lie between $C$ and $f$.


Distance of the object from the focus is :
$x=f+d_1$
Distance of image from the focus is :
$y=f-d_2$
Using Newton's formula for mirror :
$xy=f^2$
$(f+d_1)(f-d_2)=f^2$
$f^2-f{d}_2+f{d}_1-d_1{d}_2=f^2$

$\Rightarrow f=\frac{d_1{d}_2}{d_1-d_2}$

$\Rightarrow R=\frac{2d_1{d}_2}{d_1-d_2}$