The Correspondence Principle
The only reason we don’t usually notice diffraction of light in everyday life is that we don’t normally deal with objects that are comparable in size to a wavelength of visible light, which is about a millionth of a meter. Does this mean that wave optics contradicts ray optics, or that wave optics sometimes gives wrong results? No. If you hold three fingers out in the sunlight and cast a shadow with them, either wave optics or ray optics can be used to predict the straightforward result: a shadow pattern with two bright lines where the light has gone through the gaps between your fingers.
Wave optics is a more general theory than ray optics, so in any case where ray optics is valid, the two theories will agree. This is an example of a general idea enunciated by the physicist Niels Bohr, called the correspondence principle: when flaws in a physical theory lead to the creation of a new and more general theory, the new theory must still agree with the old theory within its more restricted area of applicability. After all, a theory is only created as a way of describing experimental observations. If the original theory had not worked in any cases at all, it would never have become accepted.
In the case of optics, the correspondence principle tells us that when λ/d is small, both the ray and the wave model of light must give approximately the same result. Suppose you spread your fingers and cast a shadow with them using a coherent light source. The quantity λ/d is about 10 –4, so
the two models will agree very closely. (To be specific, the shadows of your fingers will be outlined by a series of light and dark fringes, but the angle subtended by a fringe will be on the order of 10–4 radians, so they will be invisible and washed out by the natural fuzziness of the edges of sunshadows, caused by the finite size of the sun.)
Self-Check
What kind of wavelength would an electromagnetic wave have to have in order to diffract dramatically around your body? Does this contradict the correspondence principle?
It would have to have a wavelength on the order of centimeters or meters, the same distance scale as that of your body. These would be microwaves or radio waves. (This effect can easily be noticed when a person affects a TV’s
reception by standing near the antenna.) None of this contradicts the correspondence principle, which only states
that the wave model must agree with the ray model when the ray model is applicable. The ray model is not applicable here because λ/d is on the order of λ.
參考答案:对应原理
日常生活中我们一般注意不到光的衍射，唯一的原因是我们通常接触不到与可见光波长大小（即百万分之一米左右）相当的物体。那么，是不是光波学与光线学矛盾呢？还是光波学有时会出错？都不是的。如果你对着光并起三根手指，遮出一片阴影，不管用光波学还是用光线学都可以简单明了地预测阴影的形状：阴影中夹着两道明亮的光线，那是由指缝漏下的阳光。
光波学与光线学相比更具有普遍性，因此只要是在光线学有效的情况下，两种理论都是一致的。物理学者Niels Bohr阐述普遍观念时提出一个例子，称作对应理论：当一个物理理论的瑕疵引出一个新的，更普遍的理论，新的理论在其更有限的适用范围内必须与旧理论一致。毕竟，理论只是对于实验观察的描述，如果旧理论不是普遍适用，则它不可能被普遍接受。
就光学而言，对应理论告诉我们，如果λ/d值很小，那么光的波和射线模型结果就相近似。假设你张开手指，制造一个光的相干辐射源，形成一片阴影。λ/d的值大约是10 –4，这样两种模型结果就非常相近。（具体来说，手指会形成这样的阴影：周围是一系列光边和暗边，但由于每条边对应的角都符合10–4弧度，我们看不见这些边，因为太阳大小有限，自然界对于阳光造成的阴影的边界会产生模糊作用）
自我检查
要让电磁波在你身体周围产生明显的衍射，波长应该是多少呢？这与对应原理矛盾吗？
它的波长应该以厘米或米计，即与你身体的线性比例相当。它应该是微波或者无线电波。（生活中常有此类现象：人站在天线附近可以感觉到电视在接收信号。）这与对应原理一点也不矛盾，因为对应原理是说只有当光线学有效时，光波学应与光线学一致，而此处光线学不适用，应为λ/d值近似于λ 。
