10(T)%20-%20Ray%20Optics%20and%20Optical%20Instruments - 10...

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10 - RAY OPTICS AND OPTICAL INSTRUMENTS Page 1 10.1 Laws of reflection ( applicable to both the plane as well as the curved surfaces ) ( 1 ) The angle of incidence is equal to the angle of reflection. ( 2 ) Incident ray, reflected ray and the normal drawn at the point of incidence are in the same plane. 10.2 Reflection of Light by Spherical Mirrors Concave mirror is formed by making the inner surface of the circular cross-section of a spherical shell reflecting while the convex mirror is formed by making the outer surface reflecting. Some definitions with reference to the mirror ( Refer to the figures as under. ) ( 1 ) Pole ( P ) - centre of the reflecting surface ( 2 ) Principal Axis - the imaginary line passing through the pole and centre of curvature of the mirror ( 3 ) Aperture ( QQ’ ) - diameter of the reflecting surface ( 4 ) Principal Focus - the point where the rays parallel to the principal axis meet ( concave mirror ), or appear to meet ( convex mirror ), after reflection ( 5 ) Focal Plane - plane passing through the principal focus and normal to the principal axis ( 6 ) Focal Length - the distance between the pole and the principal focus ( 7 ) Paraxial Rays - rays close to the principal axis
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10 - RAY OPTICS AND OPTICAL INSTRUMENTS Page 2 10.3 Relation Between Focal Length and Radius of Curvature As shown in the figure, a paraxial ray is incident at point Q on a concave mirror. θ = angle of incidence = angle of reflection = CQF = QCF ( by geometry ) So, for CFQ, exterior QFP = CQF + QCF = 2 θ . For paraxial incident ray and small aperture, CP’ CP = R and FP’ FP = f. For small aperture, 2 θ is very small. from the figure, 2 θ FP QP = f QP ( 1 ) and θ = CP QP = R QP ( 2 ) From equations ( 1 ) and ( 2 ), R = 2f f = R / // 2 Thus, focal length of a concave mirror is half its radius of curvature. Sign Convention Sign convention for the object distance ( u ), image distance ( v ), focal length ( f ) and radius of curvature ( R ) in the formulae to be derived are as under. ( 1 ) All distances are measured on the principal axis from the pole of the mirror. ( 2 ) Distance in the direction of incident ray is positive and opposite to it negative. ( 3 ) Height above the principal axis is positive and below it is negative. Mirror Formula As shown in the figure, a ray from object O, at a distance u, is incident at point Q on the concave mirror of small aperture making an angle α with the principal axis. It gets reflected in the direction Q Ι making the same angle θ with the normal CQ as the incident ray. Another ray from O, moving along the axis, is incident at point P and gets reflected in the direction PC. Both
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This note was uploaded on 11/28/2011 for the course PHYSICS 300 taught by Professor Smith during the Spring '06 term at ITT Tech Flint.

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10(T)%20-%20Ray%20Optics%20and%20Optical%20Instruments - 10...

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