Waves and wavelets

It’s all here

Huygen’s principle – the notion that a plane wave in an isotropic medium consists of a large number of adjacent circular disturbances – wavelets- which summate in space and time to make a new wavefront can be used to explain reflection, refraction, diffraction and so on.

This is a beautiful little applet which explains refraction perfectly. More to follow later.

Take a look

Reflection: Each point on a plane wavefront can be considered to be a circular ripple. The time taken for the ripple at A to get to B is the same as the time taken for the ripple at C to get to D. The speed is unchanged in the medium, so simple geometry shows that the angle of incidence equals the angle of reflection.

Refraction: Imagine a column of soldiers, marching in step on a road. Suddenly, the road becomes muddy on one side. They’ve all been told that AT ALL COSTS they have to march in step (frequency doesn’t change). The only way they can manage is that the ones in the mud march with smaller steps (shorter wavelength, lower speed). The result is that the whole line changes direction.

Light passing from a less to more optically dense material will go more slowly. The ratio of speeds (fast to slow) is called the refractive index,n, between the two materials. From air to water n=1.33

Another way of looking at refraction (thanks to Richard Feynman) is the lifeguard on the beach who has to reach the drowning swimmer in the water. He can run faster than he can swim, so what path does he have to take to reach the swimmer in the shortest possible time?

This is a neat analogy of  Fermat’s principle or the principle of least time – the idea that the path taken between two points by a either a lifeguard needing to get to a drowning swimmer or a ray of light is the path that can be traversed in the least time, which turns out to look like the standard diagram showing refraction between two media – the beach being the less ‘optically dense’ than the sea.

This is Dick Feynman’s original diagram (supposedly)


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