Simple Nature - Light and Matter

the mechanical model would predict that a motorcycle would gostraight, and a motorcycle seems like a better approximation to aray of light than a car. The whole thing is just a model, not adescription of physical reality.j / A derivation of Snell’s law.A derivation of Snell’s lawHowever intuitively appealing the mechanical model may be,light is a wave, and we should be using wave models to describerefraction. In fact Snell’s law can be derived quite simply fromwave concepts. Figure j shows the refraction of a water wave. Thewater in the upper left part of the tank is shallower, so the speedof the waves is slower there, and their wavelengths is shorter. Thereflected part of the wave is also very faintly visible.In the close-up view on the right, the dashed lines are normalsto the interface. The two marked angles on the right side are bothequal to θ 1 , and the two on the left to θ 2 .Trigonometry givessin θ 1 = λ 1 /hsin θ 2 = λ 2 /h .andEliminating h by dividing the equations, we findsin θ 1sin θ 2= λ 1λ 2.The frequencies of the two waves must be equal or else they wouldget out of step, so by v = fλ we know that their wavelengths are774 Chapter 12 Optics