**Answer the following question.**

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

#### 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.