Thin Lenses Curved Surfaces Light striking a curved

Thin Lenses

Curved Surfaces ] Light striking a curved surface is refracted in different directions at the surface. ] Some curves will cause light rays from one point to become parallel after the interface. • Hyperbolic surface • nt > ni • Starting point is the focal point air glass

Converging Lens ] If the glass has a curved ] The light rays cross at a point surface on the other side light will bend again. beyond the lens. • Focal point for second surface • Convex or converging lens ] Concave surfaces form diverging lenses. air glass air

Radius of Curvature ] Lenses shaped like parts of spheres are easy to make. • Easy to calculate rays ] Bending comes from Snell’s Law. R f • • Assume small part of sphere Radius of curvature R Focal point f Index for air is 1

Thin Lens ] A thin lens combines two ] Rays from a point converge on spherical surfaces. • • • the other side. • Object distance so • Image distance si Different radii Curve to left R 1 Curve to right R 2 so object R 1 si image

Lensmaker’s Formula ] The object and image distances are related to the curvatures and index. ] The relationship is called the lens equation of lensmaker’s formula. • Positive curves face the object R 2 so object R 1 si image

Image Point ] A point of light lies on the central axis 120 cm to the left of a biconvex lens. ] The radii of the lens are 60 cm and 30 cm and the index of refraction is 1. 5. ] Try both directions. • n = 1. 5 • so = 1. 20 m • First R 1 = 0. 60 m, R 2 = -0. 30 m • R 2 curves away ] Where is the image? ] Does the lens direction matter? • si = 0. 60 m ] Flip, R 1 = 0. 30 m, R 2 = -0. 60 m • Same result

Thin Shapes ] Thin lenses come in a number of combinations depending on the shape of each side. • • • Convex Planar Concave next