Problem 1.382

The photon energy in the frame \(K\) is equal to \(\varepsilon .\) Making use of the transformation formulas cited in the foregoing problem, find the energy \(\varepsilon^{\prime}\) of this photon in the frame \(K^{\prime}\) moving with a velocity \(V\) relative to the frame \(K\) in the photon's motion direction. At what value of \(V\) is the energy of the photon equal to \(\varepsilon^{\prime}=\varepsilon / 2 ?\)