The distance of an object from the principal focus of a concave mirror of focal length F is D. The ratio of the size of image to the size of object is
a) F/D
b) (F/D)²
c) (F/D)^1/2
d) F+D/F-D

Dear Student ,
Here in this case the object distance , u = D and the focal length is f = F .
Now let us take that the image distance is v .
So applying the equation of spherical mirror we get ,
$$\begin{gathered} \frac{1}{v}+\frac{1}{u}=\frac{1}{f} \\ \Rightarrow \frac{1}{v}+\frac{1}{D}=\frac{1}{F} \\ \Rightarrow \frac{1}{v}=\frac{1}{F}-\frac{1}{D}=\frac{D-F}{FD} \\ \Rightarrow v=\frac{FD}{D-F} \\ Now as we know that the magnification is , m=\frac{Image dis\tan ce}{Object dis\tan ce}=\frac{Image size}{Object size} \\ So , \frac{v}{u}=\frac{Image size}{Object size} \\ \Rightarrow \frac{Object size}{Image size}=\frac{\frac{FD}{D-F}}{D}=\frac{FD}{D(D-F)}=\frac{F}{(D-F)} \end{gathered}$$
Regards