## Huygensprinciple and refraction

Light changes direction when it enters from a less dense into a denser medium. We have seen in Chapter 3 that this is governed surface glass air surface glass air

Figure 8.3 Huygens' principle and refraction.

by Snell's law of refraction, which can be derived on the basis of the assumption that light always chooses the path which takes the shortest time. We will now show using Figure 8.3 that the same law can be derived on the basis of the wave theory, using Huygens' construction.

A and C are points on an incoming plane wave front approaching the surface of a denser, yet transparent, medium such as glass or water. The spherical secondary wavelet travelling into the glass from point A has travelled a distance AD by the time point C on the wave front reaches the surface. The common tangent to all the secondary wavelets between A and B at this instant passes through points D and B and this, according to Huygens' principle, forms the new wave front. Since the wave travels more slowly in glass than in air, AD < CB, the angle d2 < d1 and the wave is bent towards the normal.

Snell's law follows directly from the construction in Figure 8.3: If light travels at a speed v1 in air and at a speed v2 in glass, where t is the time for the light to travel from C to B (or from A to D).

The triangles CAB and DAB are right-angled, so and and

sin d2 v 2

sin 92

sin9

The fact that light bends inwards towards the normal on entering a denser medium supports the argument that it behaves as a wave and not as a particle. A bullet, for example, when it enters water at an angle, slows down but keeps its original direction. Perhaps we could say that 'on the balance of probability' refraction can be taken as evidence for the wave theory. However, it is hardly evidence beyond reasonable doubt for the wave theory, to the exclusion of the particle theory!

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