互成角度的两平面镜成像问题的讨论

A Discussion on the Formation of Image for Two Angular Plane Mirror

夹角为θ的平面镜M和N之间放置一物点P,由反射所成的虚像设为K个,这些像均分布在同一个圆周上,像的总数K=[(180°-α)/θ]+[(180°-β)/θ]。当180°/θ为整数时,K个虚像中有两个像重合,故只有K-1个虚像能被看到;当180°/θ不为整数时,K的值既取决于平面镜M和N之间的夹角,还与物点P所放位置有关。

An object P is disposed between two angular plane mirror M and N at the angle of θ. Suppose the number of illusory images is K (K is integer). Two conclusions can be drawn that these images are all distributed on a circle and K is satisfied with the equation K=[(180°-°α)/θ]+[(180°-β)/θ]. When the variable 180°/θ is integer, the number of illusory images is (K-1), for there are two images are coincident. When the variable 180°/θ is not integer, the amount of K is not only relevant to the angle θ, but also depend on the position of the object P.