费马原理在旋转二次曲面理想成像中的应用——主轴上物点

APPLICATION OF FERMAT’S PRINCIPLE IN IDEAL IMAGING AT THE ROTATIONAL CONICOID BOUNDARY FOR THE OBJECT POINT INSIDE THE PRINCIPAL AXIS

运用费马原理推导出主轴上物点经旋转二次曲面反射和折射的会聚光线方程和发散光线方程,并在近轴条件下得到相应的实像和虚像的物像公式。结果表明主轴上物点经旋转二次曲面反射和折射的会聚光线方程与发散光线方程不同,而实像和虚像在新笛卡尔坐标系中的物像公式具有相同的形式。另外,当偏心率等于零时,所有方程均退化到球面界面的形式。

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,in this paper,a method has been given to directly obtain the equations for the practical optical path in reflections and refractions at the rotational conicoid boundary for the object point inside the principal axis,and then the object-image formulas have also been derived in the condition of axial ray.The present results show the equations for divergent lines are different from those for convergent lines,but the object-image formula of the real image and the virtual image has the same form in the framework of new Cartesian coordinates.In addition,all the equations degenerate to the form of spherical interface,when the eccentricity equals zero.