三棱镜最小偏向角公式的一种证明方法

A method of proving the minimum deviation angle formula in triangular prism

利用光的折射定理及光在三棱镜中折射的三角关系,推导出偏向角的函数表达式,接下来,分别作出不同的折射率及不同顶角时候偏向角的函数图像,由图像可知,偏向角的函数仅有一个极值点,且为最小值。然后利用函数求导求极值的方法,得出三棱镜偏向角为最小时的条件,并由此,求得三棱镜最小偏向角公式。

Using the theorem of refraction of light and refraction triangle of light in the triangular prism, the function expression of deviation angle is deduced. Then, we plot out the graph of the function with different apex angle and refractive index respectively. The image shows that the function only has one extreme value point, which must be the minimum value. Finally, by using the derivation method of the extremum problems of functions, we get the conditions of the minimum deviation angle of triangular prism, Use of these conditions, triangular prism minimum deviation angle formula is obtained.