S.T f=`(R )/(2)` in the case of a spherical mirror where symbols have their usual notations

Explanation

From the figure `tan theta=(MD)/(CD)`
For small angles `tantheta^(@)= theta `(rad)
`therefore theta("rad") =(MD)/(CD)" " `.........(1)
Also, `tan 2theta=(MD)/(FD)`
for small angles, `tan 2theta^(@)=2theta("rad")=(MD)/(FD)" "`............(2)
Using (1) and (2) we can write
`2((MD)/(CD))=(MD)/(FD)`
i.e. `CD=2FD`
i.e. `R=2f or f=(R)/(2)`