Phy Chapter 1 Rflection In Curved Mirrors Caltec S.3

RFLECTION IN CURVED MIRRORS 14.31 Curved Mirrors Curved mirrors are mirrors whose surfaces are obtained from a hollow transparent sphere or pipe and silvering one of the side. (a) Types of Curved Mirrors There are two types of curved mirrors, namely: Concave mirror Convex mirror (b) Reflection of parallel beams from curved mirrors (c) Terms Used The Centre of curvature, C, is the centre of the sphere of which the mirror is a part. The radius of curvature, r, is the radius of the sphere. The pole, P, of a mirror is the centre of reflecting surface. The principal axis is the imaginary line joining the pole and the centre of curvature produced in each case. The principal focus, F, is the point on the principal axis through which rays parallel and close to the principal axis pass after reflection (for the case of concave mirror) or from which the rays appear to come (for the case of convex mirror). The focal length, f, is the distance between the principal focus and the pole of the mirror. Notes: - C and f of a concave mirror - are real (i.e. are in front of the mirror). - C and f of a convex mirror - are virtual (i.e. are behind the mirror). (d) The Relation between f and r From the laws of reflection ABC = CBF But ABC = BCF (alternate angles) CBF = BCF BF = FC (sides of an isosceles triangle) Now B is very close to P BF = PF PF = FC f = or r = 2f (e) Mirrors of Large aperture If a parallel beam parallel to the principal axis is incident on to a concave mirror, the rays which are close to the principal axis are reflected to pass through the principal …