Prove R=2f..!

Dear student

 

 

Consider a ray of light AB, parallel to the principal axis, incident on a spherical mirror at point B. The normal to the surface at point B is CB and CP = CB = R, is the radius of curvature. The ray AB, after reflection from mirror will pass through F (concave mirror) or will appear to diverge from F (convex mirror) and obeys law of reflection, i.e., i = r.

 

From the geometry of the figure,

 

 

 

If the aperture of the mirror is small, B lies close to P, \ BF = PF

 

or FC = FP = PF

 

or PC = PF + FC = PF + PF

 

or R = 2 PF = 2f

 

 

Similar relation holds for convex mirror also. In deriving this relation, we have assumed that the aperture of the mirror is small.

 

 

 

 

 

 

 

 

 

 

 

Hope this helps.

Regards

Team

Topperlearning