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Question
Wed December 12, 2012 By: Rishav Singh

# For lenses i it true that the r=2f?how?

Wed December 12, 2012

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.

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