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 surfaceHyperbolic surface n t > n in t > n i Starting point is the focal pointStarting point is the focal point airglass

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

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

Thin Lens  Rays from a point converge on the other side. Object distance s o Image distance s i soso R2R2  A thin lens combines two spherical surfaces. Different radiiDifferent radii Curve to left R 1Curve to left R 1 Curve to right R 2Curve to right R 2 R1R1 sisi objectimage

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 objectPositive curves face the object soso R2R2 R1R1 sisi objectimage

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.  Where is the image?  Does the lens direction matter?  Try both directions. n = 1.5 s o = 1.20 m First R 1 = 0.60 m, R 2 = m R 2 curves away s i = 0.60 m  Flip, R 1 = 0.30 m, R 2 = m Same result

Thin Shapes  Thin lenses come in a number of combinations depending on the shape of each side. ConvexConvex PlanarPlanar ConcaveConcave next