Surface_Power,_Thin_Lens_&_Lens_Form

Surface Power, Thin Lens & Lens Form Surface Power • We now know that the power of a lens is the reciprocal of its focal length, in meters. • Today we’ll look at surface powers and the factors affecting surface power. Surface Power • The power of a surface depends on: 1. the curvature of the surface and 2. the refractive index of the material. Curvature • If we consider that the surface of the lens is a part of a circle. The centre of the circle is referred to as the centre of curvature (C). • The radius of curvature is the radius of the circle and is measured from the surface of the lens to the centre of curvature. Radius of curvature (r) Centre of Curvature (C) Curvature • The curvature of the surface (R), in Dioptres, is related to the radius of curvature of the surface in meters (r). • The greater the radius of curvature the flatter the surface, and the smaller the curvature. R=1 r 2. Refractive Index • The ratio between the speed of light in air and its speed in a particular medium is called it’s refractive index. Refractive index = velocity of light in air velocity of light in medium Refractive index = n Convex Surface F (D) r (m) Optic axis C n n’ In this case, using the sign convention, the radius of curvature will be positive (radius is measured from the surface to the centre of curvature) Concave Surface F (D) r (m) Optic axis C n n’ In this case, using the sign convention, the radius of curvature will be negative (radius is measured from the surface to the centre of curvature) • So: F = n’ – n F = Dioptres r r = metres • Remember: “refractive index of the medium which the light is about to enter minus the refractive index of the medium which the light is leaving” Thin Lens • A lens has two surfaces separated by a thickness of glass. • For now, we’ll assume the lens to be thin. • So, the first surface is F1 and the second surface is F2. • Hence, the total power of a thin lens will simply be the sum of the two surfaces. • i.e. F = F1 + F2 Surface Power & Form F1 r2 C2 n r1 C1 Optic Axis F2 Surface Power & Form F1 = Front surface power (D) F2 = Back surface power (D) C1 = Centre of curvature of F1 C2 = Centre of curvature of F2 r1 = Radius of curvature of F1 r2 = Radius of curvature of F2 n = Refractive index of the lens material. Note the lens is always in air which has a refractive index of 1. Equations for the two surfaces of the lens • F1 = (n-1) r1 • F2 = (1-n) r2 * r in metres Lens Form • A lens can be made up in a number of different forms. Types of convex lens Plano-convex Bi-convex Equi-convex Curved lens Types of convex lens (+5.00D) Plano-convex +2.50D +2.50D Bi-convex e.g. +11.00D e.g. -6.00D +5.00D 0.00D Equi-convex e.g. e.g. +4.00D +1.00D Curved lens (meniscus) Types of concave lens Plano-concave Bi-concave Equi-concave Curved lens (meniscus) Types of concave lens (-5.00D) Plano-concave Bi-concave e.g. +6.00D e.g. -11.00D -2.50D -2.50D 0.00D -5.00D e.g. -1.00D e.g. -4.00D Equi-concancave Curved lens (meniscus) Task • State the surface powers required to produce a -7.00D lens in the following forms and sketch each lens. • a. Equi-concave • b. Bi- concave • c. Plano-concave • d. Periscopic • e. Meniscus ( with a 6.00D base) • Repeat the above exercise for a +8.00D lens.