Problem 5.211

A train of plane light waves propagates in the medium where the phase velocity \(v\) is a linear function of wavelength: \(v=\) \(=a+b \lambda,\) 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 \(\tau=1 / b\).