# Useful Formulae

42 LIGHT refraction, lenses and relativity Light travelling from air into water is shown opposite. If v1 and v2 are the speeds that light takes in any two media then Snells Law of Refractionstates that for a given frequency constant or n1 sin1 n2 sin2 where n1 and n2 are the refractive indices of the two media varying slightly for different frequencies. Here are a few useful values Vacuum and air1 Water1.33 Quartz1.45 Crown glass1.52 Various lenses are shown opposite, some converging, others diverging. The focal length,f,is shown for one. TheGaussian Lens Equationrelates the distances between an object, the lens, and the upsidedown focused image 1 Here R1 and R2 are the left and right radii of curvatureof the lens negative if concave. Visible light is a tiny part of the electromagnetic spectrumwhich also includes xrays,radio and microwaves. Einstein was able to deduce that, because light travels at a constant speed away from you irrespective of your own speed,time itself must be able to stretch and dilate This is part of hisSpecial Theory of Relativity. 1 R1 1 R2 xo 1 xi 1 v2 v1 nlens nmedium sin1 sin2 f 1 43