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Define the Term 'Focal Length of a Mirror'. with the Help of a Ray Diagram, Obtain the Relation Between Its Focal Length and Radius of Curvature. - Physics

Diagram
Short Note

Answer the following question.
With the help of a ray diagram, obtain the relation between its focal length and radius of curvature.

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Solution

The distance between the centre of a lens or curved mirror and its focus.
The relationship between the focal length f and the radius of curvature R = 2f.

Consider a ray of light AB, parallel to the principal axis and 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 a mirror, will pass through F (concave mirror) or will appear to diverge from F (convex mirror) and obeys the law of reflection i.e. i = r.

From the geometry of the figure,
∠BCP = θ = i
In D CBF, θ = r
∴BF = FC (because i = r)
If the aperture of the mirror is small, B lies close to P, and therefore BF = PF
Or FC = FP = PF
Or PC = PF + FC = PF + PF
Or R = 2 PF = 2f
Or f = R/2
Similar relation holds for convex mirror also. In deriving this relation, we have assumed that the aperture of the mirror is small.

Concept: Reflection of Light by Spherical Mirrors
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