All Problems

Optics of Moving Sources

Problem 5.239

A plane electromagnetic wave propagates in a medium moving with constant velocity \(V \ll c\) relative to an inertial frame \(K\). Find the velocity of that wave in the frame \(K\) if the refractive index of the medium is equal to \(n\) and the propagation direction of the wave coincides with that of the medium.

Reveal Answer
u=c/n+V1+V/cn. If V≪c, then u≈cn+V(1−1n2)u=\frac{c / n+V}{1+V / c n} . \text { If } V \ll c, \text { then } \quad u \approx \frac{c}{n}+V\left(1-\frac{1}{n^{2}}\right)
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