Abstract: Fermat's principle is a basic principle in geometrical optics，which means that the actual trajectory in the space depends on the extremum of the optical path. Based on the Fermat’s principle，a new method has been given to directly obtain the equations for the practical optical path in reflections and refractions at spherical boundary for the virtual image，and then the object-image formula have also been derived in the condition of axial ray and axial object. The present results show the equations for divergent lines are different from those for convergent lines，but their object-image formula are very same.

Key words: Fermat’s principle, spherical reflection, spherical refraction, virtual image