Why does focal length equal half the radius for small mirror apertures?

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Homework Statement



In the attached picture ,
It has been explained in my book that
" I the apeture of the mirror is small, the point P'( ponint of incidence) is very close to the point P( pole) ,Then PF(focal length)= P'F
:. PF =Fc
or PF=1/2R"
I don't get it !
Plzzzz help!
 
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By geometry they have shown that Fc = FP'.
If P' is away from P, FP' cannot be equal to FP because it is not the radius of the spherical surface. But if P' is very close to P, FP is nearly equal ti FP'. And hence you can show that focal length of the spherical surface is R/2.