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Video abstract for the article 'Perfect imaging with geodesic waveguides ' by uan C Miñano, Pablo Benítez and Juan C González (Juan C Miñano et al 2010 New J. Phys. 12 123023). Read the full article in New Journal of Physics at http://iopscience.iop.org/1367-2630/12/12/123023/fulltext/. GENERAL SCIENTIFIC SUMMARY Introduction and background. The Maxwell fish-eye (MFE) lens is a positive, isotropic refractive-index distribution that has been well studied in the geometrical optics framework. The rays issuing from any point of space in the MFE lens are perfectly focused on another point called the conjugate of the first one. Recently, it has been proven that this refractive-index distribution also focuses waves perfectly, and super-resolution (i.e., resolving objects much smaller than the wavelength) has been claimed. On the other hand, transformation optics provides the tools to obtain a new optical medium from an original one using a mapping between the initial and final spaces that intimately links the wave propagation in both media. Main results. With the help of transformation optics we proved that a spherical waveguide filled with an isotropic non-magnetic medium, one with radial refractive index n = 1/r, has radial polarized modes with the same perfect focusing properties as the MFE lens. Moreover, the medium can be approximated by a homogeneous one if the waveguide is thin enough. These results provide a simple way to attain super-resolution experimentally. Wider implications. More general geodesic waveguides designed with the tools of geometrical optics, from a two-dimensional refractive index distribution, not only map rays in geodesic curves but also replicate the z-polarized electric fields obtained in the cylindrical refractive index distribution of the waveguides.