 Solution

ID: past-exam-of-the-physics-2-paper-of-the-university-of-oxford/2014/6/solution

Huygens' principle treats each point of a wavefront as the source of a secondary wavelet. The later wavefront is the common forward envelope of those wavelets. Consider a plane front reaching a flat interface between media with speeds

v_{1}

and

v_{2}

. In the same interval

Δ t

, the incident front advances

v_{1} Δ t

while the first transmitted wavelet grows to radius

v_{2} Δ t

The two right triangles sharing the interface segment of length

d

give

d sin i = v_{1} Δ t

and

d sin r = v_{2} Δ t

, where

i

and

r

are ray angles to the normal. Hence

\frac{s i n i}{s i n r} = \frac{v _{1}}{v _{2}} = \frac{n _{2}}{n _{1}}, n_{1} sin i = n_{2} sin r .

This is Snell's law. The frequency is unchanged at a stationary interface, while wavelength changes with the propagation speed.

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