惠更斯-菲涅耳原理

HUYGENS-FRESNEL PRINCIPLE

惠更斯-菲涅耳原理

目录

The One---The Origin of the Huygens-Fresnel principle

The Two ---The Essence of the Huygens-Fresnel principle

The Three---The Conclusion of the Huygens-Fresnel principle

一、惠更斯-菲涅耳原理的起源

二、惠更斯-菲涅耳原理的本质

三、惠更斯-菲涅耳原理的结论

The One---The Origin of the Huygens-Fresnel principle

一、惠更斯-菲涅耳原理的起源

The penetration of light waves into the region of a geometrical shadow can be explained with the aid of Huygens'principle.This principle,however,gives no information on the amplitude and ,consequently,on the intensity of waves propagating in different directions. The French physicist Augustin Fresnel (1788~1827) supplemented Huygens'principle with the concept of the interference of secondary waves.Taking into account the amplitudes and phases of the secondary waves makes it possible to find the amplitude of the resultant wave for any point of space .Huygens'principle developed in this way was named the Huygens-Fresnel principle

光波进入几何阴影区的渗透可以用惠更斯原理.这个原理虽然没有给出振幅信息.因此，对在不同方向上传播的波的强度。法国物理学家奥古斯丁-菲涅耳（1788 ~ 1827）补充了惠更斯原理的次波的干涉的概念。考虑到振幅和二次波的相位使得有可能找到任何点的空间所得到的波的振幅。惠更斯原理以这种方式发展被命名为惠更斯-菲涅耳原理。

The Two ---The Essence of the Huygens-Fresnel principle

二、惠更斯-菲涅耳原理的本质

According to the Huygens-Fresnel principle .Every element of wave surface S (Fig.1.1) is the source of a secondary spherical wave whose amplitude is proportional to the size of element dS.The amplitude of a spherical wave diminishes with the distance r from its source according to the law 1/r.Consequently,the oscillation

rives from each section dS of a wave surface at point in front of this surface . Is the the phase of the oscillation where wave surface S is ,k is the wave number ,r isthe distance from surface element dS topoint Parrives from each section dS of a wave surface at point P in front of this surface . The factor

is determined by theamplitude on the light oscillation at the location of dS .The coeffcient

()00cos a kr wt r d a K dE s +-=0a ϕ

K depends on the angle between a normal n to area dS to point P. When , this coeffcient is maximum ; when , it vanishes. 根据惠更斯-菲涅耳原理。波表面的每一个元素（1.1）是一个次级球面波的源幅度与元素的大小成正比.。一个球面波的振幅是从源到垂直于1/r 的距离。因此，振荡从每个部分的波面的点P 在这个表面的前面，是相位的振荡波表面S ，k 是波数，R 是从表面元素DS 到P 点所在DS 表面之间的距离。该α因子是由在该位置的光的光振荡的幅度确定的。系数K 取决于正常区域DS 指向点P 之间的角度.当当. ,这个系数最大；当 , 它消失。

The resultant oscillation at point P is the superposition of the oscillatoins given by Eq.(1.1) taken for the entire wave surface S:

This equation is an anslytical expression of the Huygens - Fresnel principle .

在点P 产生的振荡是由（1.1）所给的例子叠加为整个波面的:

这个方程是惠更斯-菲涅耳原理分析表达。

The Huygens - Fresnel principle can be substantiated by the following reasoning .Assume that thin opaque screen Sc(Fig.1.2) is placed in the path of a light wave (we shall consider it plane for simplicity 's sake).The intensity of the light everywhere after the screen will be zero .The reason is that the light wave falling on the screen produces oscillations of the electrons in the material of the screen.

惠更斯- 菲涅耳原理可以用下面的推理证实。假设薄的不透明的屏幕SC （1.2）被放置在一个光波的路径（我们认为这是简单的缘故飞机）。在屏幕后光的强度将为零。原因是光波落在屏幕的材料产生的电子振荡以及电子发射电磁波的振荡。 The oscillations of the electrons emit electromagnetic waves. The field after the screen is a superposition of the primary wave (falling on the screen) and all the secondary waves.The amplitudes and phases of the secondary waves are such that upon superposition of these waves with the primary one , a zero amplitude is obtained at any point P after the screen .Consequently,if the primary wave produces the oscillation at point P,then the resultant oscillation produced

by the secondary waves at the same point has the form .Here

.What has been said above signifies that when calculating the amplitude of an oscillation set up at point P by a light wave propagating from a real sources .we can replace this 0a wt +2/∏=ϕ()00cos a kr wt r d a K dE s +-=0a wt +2/∏=ϕ)(⎰-=S kr wt r a K E 0cos ϕ)(⎰+-=S kr wt r a K E 0cos ϕ)cos(α+wt A prim