The far field spatial resolution of conventional optical lenses is of the order of the wavelength of light, due to loss in the far field of evanescent, near electromagnetic field components. We show that subwavelength details can be restored in the far field with an array of divergent nanowaveguides, which map the discretized, subwavelength image of an object into a magnified image observable with a conventional optical microscope. We demonstrate in simulations that metallic nanowires, nanocoaxes, and nanogrooves can be used as such nanowaveguides. Thus, an optical microscope capable of subwavelength resolution - a nanoscope - can be produced, with possible applications in a variety of fields where nanoscale optical imaging is of value.