Wavefronts and Snell’s Law of Refraction Summary Lecture 17 Wavefronts and Snell’s Law of Refraction Smaller velocity Wavefronts closer together Change in direction

Refraction (nair ~ 1, nWater = 1.33 …) 1 2 Normal 1 Medium 1 (n1) Medium 2 (n2) 2 Caused by the difference in the speed of light in medium 1 and 2 Index of Refraction n = c/v (nair ~ 1, nWater = 1.33 …) Snell’s Law of Refraction n1 sin 1 = n2 sin 2

Example A ray of light passes from air (n = 1.0) into glass (n = 1.52) and then into Jell-O. The incident ray makes a 58.0o angle with the normal as it enters the glass and a 36.4o angle with the normal in Jell-O. What is the index of refraction in Jell-O? Glass Jell-O 58.0o 36.4o

Total Internal Reflection going from a medium with large n to a medium with small n “refracted” away from normal n2 1 2 3 4 qc n1 Critical Angle: sin C = n2/n1  > C Total Internal Reflection

Lenses Lenses refract light in such a way that an image of the light source is formed. Two prisms cause incoming parallel light rays to change direction toward the principal axis Think of a lens as a combination of many prisms with “optimized” shape (spherical instead of flat) With a convex lens parallel light converges to the focal point.

Ray Tracing for Lenses Conventions Focal Length Converging Lenses (convex) Diverging Lenses (concave) Conventions Focal Length f is positive for converging lens f is negative for diverging lens

Image Characterization Type: the image is real if di is positive Conventions Focal Length f is positive for converging lens f is negative for diverging lens Object Distance do is positive if object is to the left of the lens do is negative if object is to the right of the lens Image Distance di is positive if object is to the right of the lens di is negative if object is to the left of the lens Object and Image Size ho, hi are positive if above the principal axis Image Characterization Type: the image is real if di is positive Orientation: the image is upright if hi and ho have the same sign Size: the image is reduced if | hi | < | ho |

Thin Lens Equation Magnification Equation