The authors examine the problem of determining the spatial density distribution of a magnetized plasma containing cold electrons by using the measured phase difference between the incident and reflected waves in a given frequency range. With the methods of geometrical optics the problem yields Volterra's integral equations of the first kind. If the external magnetic field is homogeneous the equations are linear; otherwise they are nonlinear. The equations are studied by numerical methods. The authors also consider the absorption of electromagnetic waves in relation to the problem of probing a plasma.