Prove R=2f..!

Asked by Sneha George | 25th Feb, 2011, 03:03: AM

Expert Answer:

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.




Answered by  | 25th Feb, 2011, 10:06: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.