A geodesic lens for waveguides formed by four concentric zones, of which the two exterior ones, having an external radius a and b, are portions of a plane surface, the central zone, having a radius d, represents the actual lens, and the remaining zone, having an external radius c, is a connecting portion without discontinuities with the contiguous portions having an external radius respectively equal to d and b, said parameters a, b, d, having been selected according to the optical characteristics of the lens to be obtained, taking into account the formulae: focal length f=ab/(a+b), aperture=2d, linear magnification X=b/a (or X=a/b according to the position of the image with respect to the source).