Prove that for a mirror or  R = 2f 




 


1) Consider a concave mirror having C is the centre of curvature and P is the pole. As shown in the diagram.



2) Suppose a parallel beam of light to the principal axis strikes at the Y position of the mirror, and after reflection it passes through the focus F.



3) Now CY is drawn where CY is perpendicular at Y position of the mirror.



4) Another perpendicular from the principal axis was drawn to the Y, so that XY is Perpendicular to CP.



5) Now from the diagram 

so

               i = r




6) As incident light is parallel to the principal axis so, angle of incident i is equal to < YCP




Therefore we get




7) Now



Now  



Now for small value






therefore

 

CX = 2 FX



We know that whenis very small X  is very close to the pole P.



Therefore FX = f

& CX = R

Therefore R = 2f 



1) In both reflection or refraction image of an object can be formed.

 

2) When lights coming from the object meets or intersect at a point after reflection or refraction, a real image of the object is formed at the point of intersection.

 

3) But a virtual image can also form if it appears that light meets after reflection or refraction.