We investigate two Riemannian metrics. Each metric is expressed through two functions, one of them depending on $x^1$ only and the other depending on $x^4$, the time, only. We compose the Ricci tensor. The functions composing the metric tensor are determined from the condition that the form of Ricci tensor corresponds to the energy-momentum tensor of the pure radiation field. This is the special case of the electromagnetic field in which the electric and magnetic three-vectors are equal and perpendicular.