关于一道光学习题的分析与思考

SOME ANALYSIS AND CONSIDERATIONS ON AN OPTICAL EXERCISE

特殊形状的棱镜在控制光路传播方面有重要的应用价值.本文首先为一道以一种特殊形状棱镜为研究对象的习题提供了更为简便的求解方法,通过几何作图画出两次反射的虚像,发现入射界面的虚像与出射界面平行,解释了偏向角恒等于某一特殊值的本质原因.然后,文章详细地从光在棱镜中的折射率、入射点的位置、入射角大小、棱镜截面形状四个方面讨论了入射光线可以按习题中给定光路传播的条件.另外,基于以上分析,本文还对入射点位置对入射光线与法线相对位置的影响,入射界面上无盲区存在时棱镜截面的形状,以及出射光线展宽等问题进行了分析和讨论.

Special shaped prisms have great value in controlling the path of light.First,the article gives another simple method to solve the problem based on a certain special shaped prism.By drawing the virtual image of twice reflection,we find the virtual image on the inci-dent plane is parallel to the final exit facet.Then we give explanation of the essential reason a-bout why the deviation angle equals to a specific value.Conditions for the light beam propa-gates along the given path in the exercise are discussed in detail from the relationships on re-fractive index,the position of incidence point,the angle of incidence,and the shape of prisms’ cross section.In addition,based on the analysis above,this paper also explore some other problems,such as the influence of the position of incidence point on the direction of incident light,the shape of prisms’ cross section with no dead zone existing,and the widening of exit ray.