The effects of rim zone on optical propagation loss of four analytical designs of geodesic lenses are studied by calculating curvature radiuses of their meridional curves for different parameters according to relations between meridional curvature radius of waveguide geodesic lense and optical propagation loss. The relation curves between optical propagation loss and effective aperture radius are obtained. For a fixed radius of lens aperture, the smaller effective aperture radius is (namely larger rim zone), the smaller optical propagation loss is. Curvature singular points are found on the joint of rim zone and true lens of the geodesic lenses described by improved analytical designs and optimal designs. The selection rule of effective aperture radius of the above geodesic lenses and range with low loss are given.