光学和几何学本来就是紧密关联相互渗透的,有些几何问题实际上也是光学问题,现在我们看一个常见的问题。已知,直线l和l同侧的两点A、B,在l上找一点P,使PA+PB最小。易知,作B点关于l的对称点B′,连AB′交l于一点,此点即为所求的点P,也就是说PA+PB最小。这个问题其实是由A点发出的光线经l上的那一点反射后过点B的问题,PA+PB的最小性是极易证明的,当然从光学角度看光走最短路线,这是众所周知的。现把上面的问题深化一下。 Optics and geometry are inherently closely interrelated, and some geometric problems are actually optical problems. Now we look at a common problem. It is known that the two points A and B on the same side of the straight lines l and l find a point P on l to minimize PA+PB. It is easy to know that for point B at point B about l’s point of symmetry, even at point AB’ intersects at point one, this point is the point P sought, which means that PA+PB is the smallest. This problem is actually a problem that the light emitted from point A is reflected by the point on l and passed through point B. The minimum of PA+PB is easily proved. Of course, the shortest route is taken from the optical point of view. This is well-known. . The above questions are now deepened.