Focal Length and Radius of Curvature

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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.

Concave Mirror

Object at Infinity

Object at Infinity

Object at 2F or C

Object at 2F or C

Object between C and F

Object at F

Object beyond C

Object between F and P

Table depicting the position and nature of the object and image

Image for a convex mirror is small, erect and diminished.

Real images form on the side of a mirror where the object is and the virtual images for on the opposite side.