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| 1. |
What is relation between radius and centre of curvature. |
| Answer» The relationship between the focal length f and radius of curvature r is 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 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 = iIn 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 = PFOr FC = FP = PFOr PC = PF + FC = PF + PFOr R = 2 PF = 2fOr f = R/2Similar relation holds for convex mirror also. In deriving this relation, we have assumed that the aperture of the mirror is small. | |