Q.
Define focal length of a concave mirror. Prove that the radius of curvature of a concave mirror is double its focal length.
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Detailed Solution
The distance between the focus and pole of the mirror is called the focal length of the mirror.
Prove R = 2f
Let F be the focus, P is the pole of the mirror R be the radius of curvature of the mirror and 'C' be its centre of curvature.
Let a ray parallel to the principal axis striking the mirror at M. Then CM will be perpendicular mirror at M. Let be the angle of incidence and MD be the perpendicular from M on the principal axis.
Then from triangle MCP,
From triangle MFD,

