Question

A train of plane light waves propagates in the medium where the phase velocity v is a linear function of wavelength: v = a + bλ, where a and b are some positive constants. Demonstrate that in such a medium the shape of an arbitrary train of light waves is restored after the time interval τ = 1/b.

Answer 1

We write

 

Suppose a wavetrain at time t = 0 has the form 

so at time t = τ the wave train has regained its shape though it has advanced by a τ.