A wave approaches a boundary between two media at an angle. The angle of incidence is i . Medium 1 A B Medium 2 C D i t seconds later, the wave has completely moved into the new medium. The angle of refraction is r . r In medium 1, the velocity of the wave is v 1. Velocity is defined by the equation 90-i i Using geometry,  CDA = r 90-rr v1tv1t Using geometry,  BAD = i Therefore, the distance BD is given by Also, the velocity of the wave in medium 2 is v 2. Therefore, the distance AC is given by v2tv2t

Medium 1 A B Medium 2 C D i r The sine ratio gives v1tv1t v2tv2t Similarly, Making AC the subject gives Therefore, This is Snell’s Law

The frequency of a wave does not change as it moves from one medium to another. Therefore, in medium 1, Substituting into Snell’s Law gives Similarly, in medium 2

Similarly, for medium 2, The refractive index (n) of a medium is the ratio of the speed of light in a vacuum (v v ) to the speed of light in that medium. Therefore, for medium 1 Therefore