Problem (1) gives 问题 （1） 给出

Therefore 因此

This is the wavelength of violet. The first diffraction maximum of violet light with wavelength will always coincide with the first minimum of red light with wavelength , no matter what the slit width is. If the slit is relatively narrow, the overlapping of the angle will be relatively large, and conversely. Therefore, each fringe is a rainbow of color except for the central maximum when white light falls on a slit.
这是紫罗兰的波长。无论狭缝宽度如何，波长 的紫光的第一个衍射最大值总是与波长 的红光的第一个最小值一致。如果狭缝相对较窄，则角度 的重叠将相对较大，反之亦然。因此，除了白光落在狭缝上的中心最大值外，每个条纹都是彩虹色。

A logical extension of Young's double-slit interference experiment is to increase the number of slits from two to a large number of . An optical component consisting of a large number of parallel, closely spaced slits- for example, as many as is not uncommon is called a diffraction grating. A diffraction grating can be used to determine the wavelength of light with high precision. Diffraction gratings are usually made by ruling equally spaced parallel grooves on a polished glass plate using a diamond-tipped cutting tool. The grooves are effectively opaque and they scatter the light and the space between the grooves behaves as a slit. Thus, the action of a diffraction grating can be described in terms of a regular array of parallel slits. The width of a slit is and the width of a groove is is called grating constant as illustrated in Fig. 15-36. Usually has orders of , meaning that there are grooves per centimeter. Gratings are widely used to measure wavelengths and to study the structure and intensity of spectral lines. Intensity patterns of bright and dark fringes can be seen on the viewing screen when monochromatic light passes through a single or double slit. The fringe patterns also result when light falls on a grating. Fig. 15-37 shows a grating with total number of slits . At any point on the screen, the available light intensity from each slit, considered separately, is given by the diffraction pattern of that slit. The diffraction patterns for each separate slit coincide with each other because parallel rays in Fraunhofer diffraction are focused on the same point of the lens' focus plane. The diffraction rays will interference with each other since they are coherent. The diffraction patterns for equals and 20 are shown respectively in Fig. 15-38. Two important changes occur when the number of slits increases:
Young 双缝干涉实验的一个逻辑扩展是将狭缝的数量从两个增加到大量 。由大量平行、紧密间隔的狭缝组成的光学元件（例如，数量 不少见）称为衍射光栅。衍射光栅可用于高精度地确定光的波长。衍射光栅通常是通过使用金刚石尖端切割工具在抛光玻璃板上划出等距的平行凹槽制成的。凹槽实际上是不透明的，它们会散射光线，凹槽之间的空间表现为狭缝。因此，衍射光栅的作用可以用平行狭缝的规则阵列来描述。狭缝的宽度 和凹槽 的宽度称为光栅常数，如图 15-36 所示。通常 有 的阶数， 表示每厘米有 凹槽。光栅广泛用于测量波长和研究光谱线的结构和强度。当单色光通过单缝或双缝时，可以在观看屏幕上看到明色和暗色条纹的强度模式。当光线落在光栅上时，也会产生条纹图案。图 15-37 显示了具有狭缝总数的光栅 。在屏幕上的任何一点，每个狭缝的可用光强度（单独考虑）由该狭缝的衍射图给出。每个独立狭缝的衍射图相互重合，因为弗劳恩霍夫衍射中的平行光线聚焦在透镜焦平面的同一点上。衍射射线会相互干涉，因为它们是相干的。 等 值和20的衍射图分别如图15-38所示。当狭缝数量增加时，会发生两个重要变化：

(1) The bright fringes become narrower and brighter;
（1）明亮的条纹变窄，变亮;

(2) Faint secondary maxima appear between fringes.
（2）条纹之间出现微弱的次级极大值。

It indicates that the diffraction pattern of a grating is total result of interference of the lights from slits and diffraction of a single slit. The more slits, the more principal maxima and the weaker the secondary maxima become. As increase, perhaps to for a useful grating, the bright fringes become very sharp and bright indeed while the secondary maxima become so
它表明光栅的衍射图是狭缝光的干涉和单个狭缝的衍射的总结果。狭缝越多，主最大值越多，次级最大值越弱。随着 增加，也许对于 有用的光栅，明亮的条纹变得非常清晰和明亮，而次级最大值则变得如此
reduced in intensity as to be negligible in their effects. We will ignore the secondary maxim in what follows and discuss the locations of the bright fringes of a diffraction grating. The optical path difference between rays from adjacent slits shown in Fig. 15-38 is
强度降低，其影响可以忽略不计。我们将在下文中忽略次要格言，并讨论衍射光栅的明亮条纹的位置。图15-38所示的相邻狭缝光线之间的光程差为

Fig. 15-36 Grating constant
图15-36 光栅常数

Fig. 15-38 Diffraction pattern for (from up to bottom)
图15-38 衍射图 （从上到下）

Fig. 15-37 Arrangement for a grating of
图15-37 光栅 的布置

where is diffraction angle. Constructive interference creates bright fringes. These sharp bright fringes which are sometimes called principal maxima will occur when
其中 是衍射角。相长干涉会产生明亮的条纹。这些尖锐的明亮条纹有时被称为主极大值，当

Where is the wavelength of incident light, is the order of the fringe (principal maximum) and corresponding to the central fringe (or central principal maximum). Eq. (15-35) is called grating equation which gives the condition necessary to obtain constructive interference for a diffraction grating in the case of normal incidence.
其中 是入射光的波长， 是条纹的阶数（主极大值）， 对应于中心条纹（或中心主极大值）。方程（15-35）称为光栅方程，它给出了在法向入射的情况下获得衍射光栅的相长干涉的必要条件。

Missing orders occur for a diffraction grating when an interference maximum coincides with a diffraction minimum of a single slit. For example, if both the conditions and are satisfied for given , the th principal maximum of the grating diffraction is coincident with the th minimum of the gle-slit diffraction. As a result, there is no the th prin-
当干涉最大值与单个狭缝的衍射最小值重合时，衍射光栅会出现缺序。例如，如果两个条件 都满足， 则光栅衍射的 主最大值与 格栅狭缝衍射的 最小值重合。因此，没有 th prin-

cipal maximum on the viewing screen, that is such bright fringe disappears.
在观看屏幕上的最大值，即如此明亮的条纹消失。

Eq. (15-35) can be used to study the dependence of the diffraction angle on the wavelength . When the grating constant keeps a constant, the diffraction angle of the th bright fringe is determined only by the wavelength . The longer the wavelength is, the lar
式（15-35）可用于研究衍射角 对波长 的依赖性。当光栅常数 保持恒定时， 第个明亮条纹的衍射角 仅由波长 决定。波长越长，波长 越长
ger the angle is. When we use white light as incident light, except for the central fringe keeps white, all the higher-orders maxima disperse white light into their rainbow of colors on the screen. The whole of all the same order fringe of the incident light emitted by a polychromatic source is called grating spectrum, the fringe on the grating spectrum is called spectrum line. The grating spectrum formed by one material is unique, that is, a kind of material has a characteristic spectrum. We can determine components of material by its grating spectrum.
蒙古角 是。当我们使用白光作为入射光时，除了中央边缘保持白色外，所有高阶最大值都会将白光分散到屏幕上的彩虹色中。由多色光源发射的入射光的所有相同阶的条纹称为光栅光谱，光栅光谱上的条纹称为光谱线。一种材料形成的光栅光谱是唯一的，即一种材料具有特征光谱。我们可以通过光栅光谱来确定材料的成分。

Example 15-13 A beam of white light ( ) falls normally on a grating, as shown in Fig. 1539. The grating constant is , the focal length is . Find the distances from the order spectrum line of violet light ( ) and the 2nd order spectrum line of red light ( ) to the centre on the screen, respectively.
实施例15-13 一束白光（ ）正常落在光栅上，如图1539所示。光栅常数为 ，焦距为 。分别求紫光的 阶谱线 （ ） 和红光的二阶谱线 （ ） 到屏幕中心的 距离。

Fig. 15-39 for Example 15-13
图 15-39 示例 15-13

Solution Assuming the diffraction angles of the 3 rd order spectrum line of the violet light and the 2 nd order spectrum line of the red light are and , respectively. The distance from them to the centre are and , respectively. From the grating Eq. (15-35), we have
解 假设紫光的 3 阶光谱线和红光的 2 阶光谱线的衍射角分别为 和 。从它们到中心的 距离分别是 和 。从光栅方程（15-35）中，我们有

From the geometry shown in Fig. 15-39, we have
从图 15-39 所示的几何形状中，我们有

We can see that is smaller than . It indicates that the 3 rd order spectrum line of the violet light is more near the central maximum line than the 2 nd order spectrum line of the red light and the two spectrums overlap with each other. Please note that when is very small (e. g. ), the relationship that is used in discussing of single-slit diffraction may not suitable for discussing of diffraction grating.
我们可以看到它 小于 。它表明紫光的3阶光谱线比红光的2阶光谱线更靠近中心最大线，并且两个光谱相互重叠。请注意，当 非常小时（例如 ），用于讨论单缝衍射的关系 可能不适合讨论衍射光栅。

Example 15-14 Light of wavelength is incident obliquely on a grating at an angle as shown in Fig. 15-40. The diffraction grating has 5000 lines per centimeter.
实施例15-14 波长 的光以一定角度 斜入射在光栅上，如图15-40所示。衍射光栅每厘米有 5000 条线。

Fig. 15-40 For Example
图 15-40 举例

(1) Find the diffraction angles for bright fringes corresponding to and , respectively.
（1）求亮条纹的衍射角分别对应于 和 。

(2) Find the highest order of maximum that can be seen. Compare it with the one in the case of normal incidence.
（2）找到可以看到的最大值的最高阶数。将其与正常发生率的情况进行比较。

Solution (1) As light is oblique incidence, the optical path difference between rays from adjacent slits in Fig. 15-40 is
解决方案（1）由于光是斜入射的，因此图15-40中相邻狭缝的光线之间的光程差为

The principal maxima will occur when
当

Eq. (15-36) is called grating equation for oblique incidence. In this problem, the grating con.
方程（15-36）称为斜入射光栅方程。在这个问题上，光栅骗局。
stant 斯坦特

From Eq. (15-36), the diffraction angle for fringe of is
由式（15-36）可知，条纹 的衍射角为

It indicates the 0th order bright fringe located below the centre of the screen.
它表示位于屏幕中心下方的 0 阶亮条纹。

The diffraction angles corresponding to fringes of and are respectively
对应于 和 条纹的衍射角分别为

and

These tell us that the distribution of bright fringes is not symmetrical.
这些告诉我们，明亮条纹的分布是不对称的。

(2) The highest order of maximum corresponds with the maximum of , that is . From Eq. (15-36), we have
（2） 最大值的最高阶数对应 于 的最大值 ，即 。从式（15-36）中，我们有

This tells us that the highest order of maximum which can be seen is the fourth-order fringe when oblique incidence occurs.
这告诉我们，当斜入射发生时，可以看到的最高阶最大值是四阶条纹。

Assuming the highest order of the spectral line is in the case of normal incidence, according to the grating equation for normal incidence
假设谱线的最高阶是在 正常入射的情况下，根据正常入射的光栅方程

we have 我们有

which means that the highest order of maximum which can be seen is the third-order fringe when normal incidence occurs,
这意味着当正常入射发生时，可以看到的最大值的最高阶是三阶条纹，

Therefore, we can observe higher order of bright fringes in the case of oblique incidence. The highest order of spectral line is only decided by the incident angle when the wavelength and the grating constant are unchanged,
因此，在斜入射的情况下，我们可以观察到更高阶的明亮条纹。当波长 和光栅常数 不变时，光谱线的最高阶仅由入射角 决定，

Diffraction comes from the wave nature of light and is determined by the finite aperture of the optical elements. An important property of any optical instrument, such as a camera or telescope, is its resolving power. Resolving power is the ability to distinguish between two closely spaced objects. We have known that light passing a small opening or a boundary of circular lens is bended so that the images are fuzzy. Diffraction fringes near the edges of in
衍射来自光的波动性质，由光学元件的有限孔径决定。任何光学仪器（例如相机或 望远镜）的一个重要特性是其分辨能力。分辨能力是区分两个紧密间隔的物体的能力。我们已经知道，通过圆形透镜的小开口或边界 的光会弯曲，因此图像是模糊的。边缘 附近的衍射条纹
ges usually make it difficult to determine the exact shape of the source. It limits the resolving power of an optical instrument because the diffraction pattern has certain intensity distribution. Fig. 15-41 shows a circular diffraction pattern formed by a small circular aperture. Note that the large central maximum (bright spot), called Airy disk, is surrounded by alternating bright and dark rings. This diffraction is of extreme importance in an optical instrument because it sets the ultimate limit on the possible magnification.
GES通常很难确定源的确切形状。它限制了光学仪器的分辨能力，因为衍射图具有一定的强度分布。图15-41显示了由小圆孔形成的圆衍射图。请注意，大的中心最大值（亮点），称为艾里盘，被交替的亮环和暗环包围。这种衍射在光学仪器中极为重要，因为它为可能的放大倍率设定了最终限制。

Fig. 15-41 Diffraction pattern of a circular aperture
图15-41 圆形孔径的衍射图

Fig. 15-42 shows that light from two sources and pass through a small circular opening in an opaque barrier. In Fig. 15-42 (a), the images of the sources and are distinguished as separate images. In this situation, the sources are said to be resolved. If they are brought closer together as shown in Fig. 15-42 (b), however, their images overlap resulting in a confused image. When the sources are so close together (or the opening is so small) that the separate images can no longer be distinguished, the sources are said to be unresolved. The resolving power of an optical instrument is a measurement of its ability to produce well-defined separate images.
图15-42显示了来自两个光源 的光，并通过 不透明屏障中的一个小圆形开口。在图15-42（a）中，图像源 和 图像被区分为单独的图像。在这种情况下，据说来源已解决。但是，如果将它们拉得更近，如图15-42（b）所示，则它们的图像会重叠，从而产生混淆的图像。当源距离如此之近（或开口如此之小）以至于无法再区分单独的图像时，则称源未解析。光学仪器的分辨能力是衡量其产生清晰定义的单独图像的能力的指标。

(a)

(b)

Fig. 15-42 (a) The images of the sources and are easily distinguished;
图15-42 （a）来源 的图像， 易于区分;

(b) As the sources are brought closer together, the images overlap, resulting in a confused image.
（b） 当来源靠得更近时，图像重叠，导致图像混淆。

It can be proved that the first minimum of the diffraction pattern of a circular aperture with a diameter (Fig. 15-43) is given by
可以证明，直径为圆形孔径 的衍射图的第一个最小值（图15-43）由下式给出

Fig. 15-43 Ariy disk
图15-43 Ariy圆盘

From Eq. (15-37) propor se that the size of the central maximum is directly portional to . That is, the central maximum is more spread out for longer wavelength and smaller aperture. No matter how perfectly a lens is constructed, the image of a point source of light will not be focused at a point. What is the condition of two images just re-
从式（15-37） 可以看出，中心最大值的大小与 成正比。也就是说，对于更长的波长和更小的孔径，中心最大值更加分散。无论镜头构造得多么完美，点光源的图像都不会聚焦在一个点上。两张图片的状况是什么，只是重新
solved? The accepted criterion for resolution is the Rayleigh criterion, first proposed by Rayleigh (1842-1919): two images are just resolved when the center of the diffraction pattern of one is directly over the first minimum of the diffraction pattern of the other. It tells us that two images are just resolved when the center of central maximum of one pattern coincides with the first dark fringe of the other. According to Rayleigh criterion and Eq. (15-37), two point objects separated by an angle are just resolved when
解决？公认的分辨率标准是瑞利准则，由 瑞利（1842-1919）首次提出：当一个图像的衍射图的中心正好位于另一个图像的衍射图的第一个最小值上时，两个图像刚刚被解析。它告诉我们，当一个模式的中心最大值中心与另一个模式的第一个暗条纹重合时，两个图像就会被解析。根据瑞利准则和方程（15-37）， 当

where is called the minimum angle in radians, is called the resolving power of an optical instrument. It depends on the wavelength of the light and the diameter of the instrument's aperture. Fig. 15-44 shows two point objects when they are clearly resolved, just resolved and
其中 称为弧度的最小角度， 称为光学仪器的分辨能力。这取决于光的波长和仪器孔径的直径。图 15-44 显示了两个点对象，当它们被清晰解析、刚刚解析和

Fig. 15-41 Two point objects when they are clearly resolved, just resolved and unresolved
图15-41 清晰解析、刚刚解析和未解析的两点对象

During the autumn of 1895 , when studying the conduction of electricity, W. K. Roent-
在1895年秋天，在研究电的传导时，W.K.伦特-

Fig. 15-45 X-ray tube gen discovered a mysterious radiation which was able to penetrate thin layers of material. He called this radiation as X-ray, with the " " standing for "unknown". But it was soon established that X-ray is a type of electromagnetic radiation with wavelength in the range of 0.01 to 10 nanometers. Fig. 15-45 shows an X-ray tube - a device causes the emission of X-ray.
图15-45 X射线管发现了一种神秘的辐射，能够穿透材料的薄层。他将这种辐射称为X射线，“ ”代表“未知”。但很快就确定 X 射线是一种波长在 0.01 到 10 纳米范围内的电磁辐射。图 15-45 显示了 X 射线管 - 引起 X 射线发射的装置。

Diffraction is a natural property of waves. The diffraction phenomena of X-ray ought to be observed. But it is very difficult to observe X-ray diffraction because the wavelength of X-ray is too small for ordinary diffraction gratings. Not all diffraction gratings are commercially made. Crystalline solids supply natural gratings. The regular array of atoms in a crystal forms a natural 3-dimensional diffraction grating with a spacing that falls in the wavelength gion of X-ray. The suggestion that crystal could be used to diffract X-ray was first made by German physicist M. Von Laue. In 1912, Laue carried out an experiment to prove the wa ware nature of X-ray. The experiment arrangement of X-ray diffraction is shown in Fi. . When a collimated beam of -rays with a continuous distribution of wavelength strikes a single cy tal, it is strongly scattered only in certain sharply defined directions. One certain pattern of spots 0 o
衍射是波的自然特性。应该观察X射线的衍射现象。但是观察X射线衍射非常困难，因为X射线的波长对于普通的衍射光栅来说太小了。并非所有衍射光栅都是商业制造的。结晶固体提供天然光栅。晶体中的规则原子阵列形成一个天然的三维衍射光栅，其间距落在X射线的波长 中。晶体可用于衍射X射线的建议最早是由德国物理学家M.Von Laue提出的。1912年，劳厄进行了一项实验，以证明X射线的威严 性质。X射线衍射的实验布置如图所示。 当具有连续波长分布的 准直射线束撞击单个射线 时，它仅在某些明确定义的方向上强烈散射。斑点 0 o 的某种模式
ours when the diffracted rays are fallen on a photographic film. These spots, called Laue Spots as shown in Fig. 15-47, are related in complicated ways to the internal structure of the crystal. The Laue spots is the diffraction pattern of X-ray through a single crystal and it verified that X-ray is a kind of wave.
当衍射光线落在照相胶片上时。这些斑点称为劳厄斑点，如图15-47所示，以复杂的方式与晶体的内部结构相关。劳厄光斑是X射线通过单晶的衍射图，它证实了X射线是一种波。

Fig. 15-46 Experiment arrangement for X-ray diffraction
图15-46 X射线衍射实验布置

Fig. 15-47 Laue spots
图15-47 劳厄斑

After soon the experiment suggested by M. Von Laue, W. L. Bragg and his father W. H. Bragg suggested another method to study X-ray diffraction. The father and his son shared the 1915 Nobel Prize for their use of X-ray to study the structures of crystals. Fig. 15-48 shows a two dimensional representation of a three dimensional crystal and the rows of dots portray planes of atoms. The X-rays of a single wavelength are in phase before being scattered from the atoms in plane and in plane . For constructive interference of the X-rays scattered from each plane of atoms, the glancing angle is equal to the emergence angle. Note that both angles are measured relative to the planes. The path difference is in Fig. 15-48 since rays scattered from the atoms in plane travels a greater distance than those scattered from the atoms in plane . Let the distance between adjacent planes be . As ,
在M. Von Laue提出的实验后不久，W. L. Bragg和他的父亲W. H. Bragg提出了另一种研究X射线衍射的方法。父子俩因使用X射线研究晶体结构而共同获得了1915年的诺贝尔奖。图15-48显示了三维晶体的二维表示，点的行描绘了原子的平面。单个波长的 X 射线在从平面 和平面 上的原子散射之前是同相的。对于从每个原子平面散射的X射线的相长干涉，掠角等于出射角。请注意，这两个角度都是相对于平面测量的。路径差如 图 15-48 所示，因为从平面 上的原子散射的光线比从平面 上的原子散射的光线传播的距离更大。设相邻平面之间的距离为 。作为 ，
we have 我们有

where is the order number of an intensity maximum. The angle of glance and emergence in above equation is also called a Bragg angle. The Waves scattered from the atoms in plane will arrive at the detector in phase with the waves scattered from the atoms in plane . An interfer-
其中 是最大强度的阶号。上式中的瞥角和涌现角也称为布拉格角。从平面 上的原子散射的波将与平面 上原子散射的波同相到达探测器。干扰器-

Fig. 15-48 X-ray diffraction-Bragg's low ence maximum appears in the direction of emergence angle . Similarly, constructive interference will occur for rays scattered from the atoms of each of many planes that are parallel to planes and . Eq. (15-40) was first developed by W. L. Bragg and is called Bragg's law. Each of the many families of planes has its own characteristic interplanar spacing . Bragg's law gives the angles which locate the maxima produced by the constructive interference of X-ray.
图15-48 X射线衍射-布拉格低值最大值出现在出射角 方向上。类似地，从平行于平面 和 的许多平面的原子中的每一个散射的光线将发生相长干涉。方程（15-40）最初由W.L.布拉格提出，被称为布拉格定律。许多平面系列中的每一个都有自己特有的 平面间距。布拉格定律给出了定位 X 射线相长干涉产生的最大值的角度。

sort of waves, such as sound waves or waves on a stretched string. As noted in Chapter 13 ,
一种波，例如声波或拉伸弦上的波。如第 13 章所述，
the sound waves and waves on a stretched string are longitudinal and transverse wave disturb.
拉伸弦上的声波和波是纵波和横波扰动。
ance, respectively. More evidence is needed to determine whether light waves are longitudinal
分别是ance。需要更多的证据来确定光波是否是纵向的
or transverse. As we will see below, the polarization is a characteristic of transver a ance, respectively. The light can be polarized gives the best evidence that light is a transverse wave.
或横向。正如我们将在下面看到的，极化分别是横向的特征。光可以偏振，这是光是横波的最佳证据。
L

Light is one type of electromagnetic wave, as noted in Chap. 14. The electromagnetic pendicular to the direction of propagation. And the directions for the oscillations of the electric and magnetic fields are always perpendicular to each other, as shown in Fig. 14-7. Polarization is an attribute that the oscillations of a wave have a definite direction relative to the direc tion of wave's propagation. Waves having such a direction are side to be polarized. For an electromagnetic wave, the polarizing direction is defined as the direction parallel to the oscillaradiation are sensitive.
光是电磁波的一种，如第14章所述。电磁垂直于传播方向。电场和磁场的振荡方向总是相互垂直的，如图14-7所示。极化是一种属性，即波的振荡相对于波的传播方向具有确定的方向。具有这种方向的波是偏振的一侧。对于电磁波，偏振方向被定义为平行于振荡辐射的方向是敏感的。

(a)

(b)

Fig. 15-49 (a) Random polarization
图15-49 （a） 随机偏振

(c) one polarized light (the beam molarized light is showed diagrammatically;
（c）一束偏振光（光束摩尔化光以示图方式表示;

moving out of the plane of the page)
移出页面的平面）

composed of many waves with all or the sun light are randomly polarized as they ard light or unpolarized light. Nature directions of polarization. Such light is called natur large number of atoms and moleculation mechanism. tation of the electric fields prillate independently so that the oriel ly, we can represent unpolarized ly, as shown in Fig. 15-49 (a). It is by double arrow electric field vector oriented randol
由许多波组成，所有或太阳光都是随机偏振的，因为它们是光或非偏振光。极化的性质方向。这种光被称为天然的大量原子和分子机制。电场的 tation 独立地进行，因此 oriel ly，我们可以表示非极化的 ly，如图 15-49 （a） 所示。它是由双箭头电场矢量 定向的兰多尔
components, but the phase difference between them is random, as shown in Fig. 15-49 (b). Logically, the polarized light can be represented by a double arrow electric field vector , as shown in Fig. 15-49 (c).
分量，但它们之间的相位差是随机的，如图15-49（b）所示。从逻辑上讲，偏振光可以用双箭头电场矢量表示 ，如图15-49（c）所示。

Fig. 15-50 Polarizing direction
图15-50 偏振方向

A wave can be polarized by use of a polarizing filter which acts as a polarizing slit for light. A polarizing filter allows just only polarization in one to pass through. The axis of a polarizing filter (also called polarizing direction) is the direction along which the filter passes the vector of light, as shown in Fig. 15-50. In fact, the polarizing direction of a light wave is defined to be the direction of its electric field.
波可以通过使用偏振滤光片进行偏振，该滤光片充当光的偏振狭缝。偏振滤光片只允许一个偏振通过。偏振滤光片的轴（也称为偏振方向）是滤光片通过光矢量 的方向，如图 15-50 所示。事实上，光波的偏振方向被定义为其电场的方向。

Let us place two polarizing filters in the way of light emitted from a bulb, as shown in Fig. 15-51. The polarizing filters and are usually called a polarizer and an analyzer, respectively. The polarizing directions of and are represented by the parallel lines in filters. If we rotate about the direction of propagation of light, the intensity of light transmitted from varies with angle , as shown in Fig. 15-51 (a). Two positions where the polarizing directions and are at right angle exist so that the transmitted light intensity is almost zero. This fact reveals the light emerging from is polarized. The light can be polarized gives the good evidence that light is a transverse wave. Furthermore, if we remove and rotate , the transmitted light intensity
让我们在灯泡发出的光中放置两个偏振滤光片，如图 15-51 所示。偏振滤光片 通常 分别称为偏振器和分析仪。和 的 偏振方向由滤光片中的平行线表示。如果我们 绕光的传播方向旋转，透 射的光强度随角度 变化，如图15-51（a）所示。偏振方向 和 直角的两个位置存在，因此透射光强度几乎为零。这一事实表明，从 中发出的光是偏振的。光可以偏振，这很好地证明了光是横波。此外，如果我们移除 并旋转 ，透射光强度

(a)

(b)

Fig. 15-51 (a) The light transmitted from is polarized; (b) the light emitted from a bulb is unpolarized keeps unvarying, which shows that light emitted from ordinary light sources such as bulb or the sun is unpolarized.
图15-51 （a） 透射光 为偏振光;（b） 灯泡发出的光是非偏振的，保持不变，这表明从灯泡或太阳等普通光源发出的光是非偏振的。

As shown in Fig. 15-51, the intensity of emerging light from varies with angle . What law does it follow? Etienne Louis Malus gave the answer in 1809.
如图15-51所示，出 射光的强度随角度 而变化。它遵循什么法律？艾蒂安·路易斯·马卢斯（Etienne Louis Malus）在1809年给出了答案。

If the amplitude of the polarized light falling on is , then, the amplitude of the light that emerges is , where is the angle between the polarizing directions of and . Since the intensity of light is proportional to its amplitude squared, so we have
如果落在上的 偏振光的振幅为 ，则出现的光的振幅为 ，其中 和 的偏振方向之间夹角。由于光的强度与其振幅的平方成正比，因此我们有

in which is the intensity of polarized light that incidents on is the intensity of the light that emerges from .
其中 入射的偏振光的强度 是从 中射出的光的强度。

Eq. (15-41) can be rearranged as:
方程（15-41）可以重新排列为：

which is called Malus's Law. In Fig. 15-51 (a), the maximum occurs at or . When or is rotated so that in Eq. (15-42) has value of or , the intensity of light that transmits through is a minimum, say, no light is passed.
这被称为马鲁斯定律。在图 15-51 （a） 中，最大值出现在 或 处。当 or 旋转时， 在方程 （15-42） 中具有 or 的值，透射 的光强度最小，例如，没有光通过。

Example 15-15 Unpolarized light falls on two polarizing filters placed one on top of the other. What must be the angle between the polarizing directions of two filters if the intensity of the transmitted light is one fourth of intensity of the incident beam? Assume that each polarizing filter is ideal, that is, it reduces the intensity of unpolarized light by exactly .
例 15-15 非偏振光落在两个偏振滤光片上，一个放在另一个上面。如果透射光的强度是入射光束强度的四分之一，则两个滤光片的偏振方向之间的角度必须是多少？假设每个偏振滤光片都是理想的，也就是说，它将非偏振光的强度正好 降低了 。

Solution Suppose the angle between the polarizing directions of two filters is is the intensity of incident unpolarized beam. The intensity of the light transmitted from the first filter is as the filter is ideal. According to Malus's law, the intensity of the light transmitted from the second filter is
解 假设两个滤光片的偏振方向之间的角度是 入射非偏振光束的强度。从第一个滤光片透射的光的强度与 滤光片一样是理想的。根据马鲁斯定律，从第二个滤光片透射的光的强度为

So we have 所以我们有

If you rotate a polarizing filter in front of one-eye, you can reduce or eliminate the glare from sunlight reflected from water or from any glossy surface. Such reflected light is fully or partially polarized by the process of reflection from the surface.
如果在单眼前旋转偏振滤光片，则可以减少或消除水或任何有光泽的表面反射的阳光产生的眩光。这种反射光通过表面反射过程完全或部分偏振。

Fig. 15-52 shows an unpolarized beam falling on a glass surface. The electric field vector for each wave train in the beam can be resolved into two components-a perpendicular component (perpendicular to the plane of paper), represented by dots in Fig. 15-52, and a parallel component (lying in the plane of paper), represented by straight short lines. For unpolarized incident light, these two components are of equal amplitude. It can be proved experimentally that at a particular angle of incidence, called the Brewster's angle , the reflection for the parallel component is zero, which means that the reflected light is completely polarized, as shown in Fig. 15-52. The refracted beams, however, are not completely polarized, but par tially polarized.
图 15-52 显示了落在玻璃表面上的非偏振光束。光束中每个波列的电场矢量可以分解为两个分量——垂直分量（垂直于纸平面），由图 15-52 中的点表示，以及平行分量（位于纸平面上），由直线表示。对于非偏振入射光，这两个分量的振幅相等。可以通过实验证明，在特定的入射角（称为布鲁斯特角 ）下，平行分量的反射率为零，这意味着反射光是完全偏振的，如图15-52所示。然而，折射光束不是完全偏振的，而是部分偏振的。

At the Brewster's angle (sometimes be called polarizing angle), it can be shown experi mentally that the refracted beams are at right angles with the reflected beams, or equivalently
在布鲁斯特角（有时称为偏振角）下，可以在精神上证明折射光束与反射光束成直角，或等效

From the Snell's law we have
从斯涅尔定律中，我们有

Fig. 15-52 At the Brewster angle, the reflected lights is completely polarized but of low intensity
图15-52 在布鲁斯特角，反射光完全偏振，但强度低

Combining these equations leads to
结合这些方程可以得出

or

where is the index of refraction of the medium in which the reflected light travels and is the index of refraction of the medium from which the light is refracted. Eq. (15-45) is known as Brewster's Law after Sir. David Brewster deduced it empirically in 1812.
其中 是反射光传播的介质的折射率， 是折射光的介质的折射率。方程（15-45）在大卫·布鲁斯特爵士（Sir David Brewster）于1812年根据经验推导出来后被称为布鲁斯特定律。

At the Brewster's angle, the reflected beam is of low intensity. Of the components perpendicular to the plane of incidence, about are reflected if the reflecting surface is glass. The refracted beam, which is not completely polarized, is bright. The intensity of the reflected polarized beam can be increased by combining reflections as a result of stacking several plates, as shown in Fig. 15-53. The combined refracted beam becomes less intense but more completely polarized.
在布鲁斯特角下，反射光束的强度很低。在垂直于入射平面的分量中，如果反射面是玻璃，则大约 被反射。未完全偏振的折射光束很亮。反射偏振光束的强度可以通过堆叠多块板来组合反射，如图15-53所示。组合折射光束的强度降低，但偏振更完全。

Example 15-16 One wish to use a plate of
例 15-16 一个人希望使用

Fig. 15-53 Stacking glass used to incrcease the intensity of reflected polarized light. The transmitted beam is almost polarized glass as a polarizer. (1) What is the Brewster's angle? That is, at what angle of incidence will the reflected beam be fully polarired? (2) What angle of refraction corresponds to this angle of incidence?
图15-53 用于增强反射偏振光强度的堆叠玻璃。透射光束几乎是偏振玻璃 作为偏振片。（1）布鲁斯特角是什么？也就是说，反射光束在什么入射角下会完全偏振？（2）这个入射角对应什么折射角？

Solution From Brewster's law, we have
解决方案 根据布鲁斯特定律，我们有

since 因为

Corresponding to one beam of incident light, only one beam of light emerges through a homogeneous isotropic medium, such as glass or water. If the transparent medium is an anisotropic medium, such as a nature crystal of calcite as shown in Fig. 15-54, not one but two beams of light emerging from the calcite. This phenomenon is known as double refraction, The crystals having the property of double refraction are said to be double refraction crystals, Double refraction, also called birefringence, an optical property in which one beam of unpolarized light entering an anisotropic medium is split into two rays, each traveling in a different direction. One ray that follows Snell's law is called the ordinary ray (o-ray or o-beam), the other ray does not obey Snell's law is called the extraordinary ray (e-ray or e-beam). In double refraction, the ordinary ray and the extraordinary ray are polarized vibrating at right angles to each other.
对应于一束入射光，只有一束光通过均匀的各向同性介质（如玻璃或水）出现。如果透明介质是各向异性介质，例如方解石的性质晶体，如图15-54所示，则从方解石中射出的不是一束，而是两束光。这种现象被称为双折射，具有双折射特性的晶体被称为双折射晶体，双折射，也称为双折射，一种光学特性，其中一束进入各向异性介质的非偏振光被分成两束光线，每束光线沿不同的方向传播。遵循斯涅尔定律的一条射线称为普通射线（o射线或o型束），另一条不服从斯涅尔定律的射线称为非凡射线（电子射线或电子束）。在双折射中，普通光线和非凡光线被偏振，彼此成直角振动。

Fig. 15-54 One incident beam be split into two beams
图15-54 将一个入射光束分成两个光束

(a) Negative uniaxial crystal
（a） 负单轴晶体

(b) Positive uniaxial crystal
（b） 正单轴晶体

Fig. 15-55 The wave fronts of o-ray and e-ray from a point source o in a uniaxial crystal
图15-55 单轴晶体中来自点源o的o射线和e射线的波前

Using monochromatic sodium light of and measuring the angles of incident and refraction, o-ray yields a constant index of refraction of 1.655 . However, the e-ray shows an index of refraction that varies from 1.486 to 1.655 depending on the angle of incidence. This difference suggests that the e-ray propagates through the crystal at different speeds in different directions.
使用单色钠光 并测量入射角和折射角，O射线产生的恒定折射率为1.655。然而，电子射线显示的折射率从 1.486 到 1.655 不等，具体取决于入射角。这种差异表明，电子射线以不同的速度在不同的方向上传播穿过晶体。

The double refraction phenomena can be interpreted By Huygens' principle. According to the Huygens' principle, since the speed of o-ray is the same in all directions, the secondary wavelets wave front of o-ray from a point source within a doubly refracting crystal is a spheri-
双折射现象可以用惠更斯原理来解释。根据惠更斯原理，由于 o 射线在所有方向上的速度都相同，因此来自双折射晶体内点源的 o 射线前波的次级小波是球形

The e-ray, however, has different speed in different direction, the wave front of e-asy's secondary wavelets is not a spherical surface, but an elliptical surface, as shown in Prif. 15-55. The two wave fronts of o-ray and e-ray are tangent to each other in direction ( in Fig. 15-55), which is called the optic axis of crystal. Thus the optic axis is such a direction in which the speed of o-ray and e-ray are equal. Fig. 15-55(a) represents a crystal in which the sped of o-ray is always smaller than that of e-ray in all directions is called negative uniaxial wys tral, such as Calcite and Tourmaline. Fig. 15-55 (b) represents for the positive uniaxial wrytral, such as quartz and ice, in which the speed of the o-ray is always faster that of e-ray in alldirections. In some crystals there are two different directions in which the speeds are enual. These crystals are called biaxial crystals. Almost all of the doubly refracting crystals used in optical instruments (chiefly quartz and calcite) are uniaxial, however, we will concentrate on uniaxial crystals.
然而，电子射线在不同方向上具有不同的速度，e-asy的次级小波的波前不是球面，而是椭圆面，如Prif所示。15-55. O射线和电子射线的两个波前在方向上相互切线（ 如图15-55所示），称为晶体的光轴。因此，光轴是 o 射线和电子射线速度相等的方向。图15-55（a）表示一种晶体，其中O射线的加速在所有方向上总是小于e射线的加速，称为负单轴wys tral，如方解石和电气石。图15-55（b）表示正单轴辐状物，如石英和冰，其中O射线的速度总是快于电子射线在所有方向上的速度。在一些晶体中，有两个不同的方向，其中速度是一致的。这些晶体称为双轴晶体。几乎所有光学仪器中使用的双折射晶体（主要是石英和方解石）都是单轴的，但是，我们将专注于单轴晶体。

Fig. 15-56(a), (b), (c), (d) are diagrams showing the double refraction of calcite. The and in the Fig. 15-56 is the wave front of o-ray and e-ray, respectively. The plane tormed by normal and optic axis of crystal is called the principal section of crystal. In Fig. 15-56(a), (b), (c), the principal section is the plane of page, while the principal section of Fig. (d) is perpendicular to the page. When the incidence plane (the plane formed by incident light and normal) is parallel to the principal section, the vibration planes of o-ray and eray are perpendicular and parallel to the principal section, respectively. That means their planes of polarization to be perpendicular to each other. If the incidence plane is not parallel to the principal section, the vibration planes of o-ray and e-ray are not perpendicular to each other, but the angle between them nearly equal to . Even light incidents normally on the crystal as shown in Fig. 15-56 (b), the light will also be split into two beams. When the optic axis of crystal is parallel to the crystal's surface and the light incidents normally, the o-ray and eray pass through crystal in original direction of incident, not separated, but with different speeds, as shown in Fig. 15-56 (c) and (d).
图15-56（a）、（b）、（c）、（d）是方解石双折射图。图15-56中的 和 分别是o射线和e射线的波前。由晶体的法轴和光轴撕裂的平面称为晶体的主截面。在图15-56（a）、（b）、（c）中，主截面为页面平面，而图15-56（a）、（b）、（c）的主截面为页面平面。 （d） 垂直于页面。当入射面（入射光和法线形成的平面）平行于主截面时，o射线和eray的振动面分别垂直于主截面并平行于主截面。这意味着它们的极化平面彼此垂直。如果入射面不平行于主截面，则 o 射线和 e 射线的振动平面不垂直，但它们之间的夹角几乎等于 。即使光正常入射在晶体上，如图15-56（b）所示，光也会被分成两束光束。当晶体的光轴平行于晶体表面，光正常入射时，o射线和射线以原始入射方向穿过晶体，不是分开的，而是以不同的速度穿过晶体，如图15-56（c）和（d）所示。

(a)

(b)

(c)

(d)

Fig. 15-56 Diagrams showing the double refraction of negative uniaxial crystal: Incident at arbitrary angle in (a); normally incident with different optic axis directions in (b), (c) and (d) Thes to speed difference between o-ray and e-ray has a maximum in the direction at right an"tight optic axis; it is customary to define the index of extraordinary ray in the direction ray ingles to the optic axis, i. e. the ratio of the speed of light in a vacuum to the speed of in the direction at right angles to the optic axis. Some values of and , the indices for
图15-56 负单轴晶体的双折射图：（a）中任意角度入射;通常入射到（b）、（c）和（d）中不同的光轴方向，o射线和电子射线之间的速度差在右方向上最大，在“紧光轴”;习惯上定义异常光线在光线与光轴方向上的指数，即真空中的光速与与光轴成直角的方向的速度之比。 和 的一些值，索引
ordinary ray and extraordinary ray in the direction at right angles to the optic axis are listed in Table 15-4.
与光轴成直角方向的普通光线和非凡光线列于表15-4中。

Table 15-4 Indices of refraction of doubly refracting crystals
表15-4 双折射晶体折射率

(for light wavelength )
（对于光波长 ）

Usually, the angle between o-ray and e-ray is not very large even with the highly doubly refracting crystal calcite, so that some extra technique is needed to separate them to obtain polarized light from nature light. A prism originally developed by Glan and Thompson and then modified by Ammann and Massey (1968) is such an example. The modified Glan-Thompson prism consists of a glass prism with index of refraction 1.655 and a calcite prism with index of refraction 1.486 that are cemented together by their long faces. The optical cement has the same index of refraction with glass. As shown in Fig. 15-57, where the thickness of cement is exaggerated, the natural unpolarized light incident from the left is resolved into two perpendicular components (represented by dots and double arrows). Both beams travel the same parh with equal speed in the glass. The parallel component is extraordinary ray (e-ray) in calcite with an index of refraction 1.486. It will totally internal reflected when traveling from cement ( ) toward calcite. The vertical component is ordinary ray (o-ray) in calcite with an index of refraction 1.655 and proceeds without deflection from glass to cement and to calcite. It emerges into the air on the right side since its polarization plane is perpendicular to the principal section, e. g, the plane of the page. The Glan-Thompson prism can be used as a polarizer or an analyzer, When the incident light is polarized light with its vibration plane parallel to the principal section, no transmitted light can be viewed by observer.
通常，即使使用高度双折射的晶体方解石，O射线和电子射线之间的角度也不是很大，因此需要一些额外的技术来分离它们，以获得来自自然光的偏振光。最初由 Glan 和 Thompson 开发，然后由 Ammann 和 Massey （1968） 修改的棱镜就是这样一个例子。改进的 Glan-Thompson 棱镜由折射率为 1.655 的玻璃棱镜和折射率为 1.486 的方解石棱镜组成，它们通过它们的长面粘合在一起。光学水泥与玻璃具有相同的折射率。如图15-57所示，水泥厚度被夸大，从左侧入射的自然非偏振光被分解为两个垂直分量（用点和双箭头表示）。两束光束在玻璃中以相同的速度传播相同的光束。平行分量是方解石中的非凡射线（电子射线），折射率为1.486。当从水泥 （ ） 向方解石移动时，它将完全内部反射。垂直分量是方解石中的普通射线（o射线），折射率为1.655，并且不会从玻璃转向水泥和方解石。它出现在右侧的空气中，因为它的偏振平面垂直于主部分，例如页面的平面。Glan-Thompson棱镜可用作偏振镜或分析仪，当入射光是偏振光，其振动平面平行于主截面时，观察者无法看到透射光。

Certain doubly refracting crystals exhibit dichroism, that is, one of the polarized components is absorbed much more strongly than the other. Hence, if the crystal is cut of a proper thickness, one of the components is practically extinguished by absorption, while the other is transmitted in appreciable amount, as indicated in Fig. 15-58. Tourmaline is one example of such a dichroic crystal. Dichroism is the basic operating principle of the commercial Polaroid sheet,
某些双折射晶体表现出二色性，也就是说，其中一个偏振成分比另一个成分被吸收得更强。因此，如果晶体被切割成适当的厚度，其中一个组分实际上会因吸收而熄灭，而另一个组分则以可观的量透射，如图 15-58 所示。碧玺就是这种二向色晶体的一个例子。二色性是商用宝丽来片材的基本工作原理，

Fig. 15-57 Glan-Thompson polarizing prism, as modified by Ammann and Massey
图15-57 Glan-Thompson偏振棱镜，经Ammann和Massey修改

Fig. 15-58 Plane-polarized light transmitted by a dichroism crystal
图15-58 二向色性晶体透射的平面偏振光

The two beams of light emerge from a double refracting crystal can not interfere with each other even though they could meet again. This is because their vibration directions nearly perpendicular to each other. As shown in Fig. 15-59, when a doubly refracting crystal is inserted between two crossed Polaroid sheets, the emerging beams from the analyzer are found to interfere. In Fig. 15-59, the o-vibration and e-vibration refer to ordinary ray and extraordinary ray, respectively. The polarized light falling on the crystal can be resolved into two components, -vibration and e-vibration. o-vibration and e-vibration are perpendicular and parallel to the principal section, respectively. Only the components of o-ray passes through the analyzer and e-ray still lies in its polarizing direction, so the components of o-ray and e-ray emerge analyzer and lie in the same direction of -axis in the figure. They will interfere with each other. When the two beams have an optic path difference of an odd multiple of one-half a wavelength, they interfere destructively; while the optic path difference is of even multiple of one-half a wavelength, they interfere constructively. The interference fringes will be viewed through analyzer. If the light applied is of many colors, the colorful interference fringes will appear.
从双折射晶体中射出的两束光即使可以再次相遇，也不会相互干扰。这是因为它们的振动方向几乎彼此垂直。如图 15-59 所示，当在两张交叉的宝丽来片之间插入双折射晶体时，发现来自分析仪的出现光束会发生干涉。在图15-59中，o振动和e振动分别指普通射线和异常射线。落在晶体上的偏振光可以分解为两个分量， -振动和电子振动。O-振动和电子振动分别垂直于主截面。只有O射线的分量通过分析仪，而电子射线仍然位于其偏振方向，因此O射线和电子射线的分量出现在分析仪中，并且位于图 中-轴的同一方向。它们会相互干扰。当两束光束的光程差为波长的奇数倍数时，它们会产生破坏性干扰;虽然光程差是二分之一波长的倍数，但它们具有建设性的干涉作用。干涉条纹将通过分析仪查看。如果施加的光是多种颜色的，则会出现彩色干涉条纹。

Fig. 15-59 A diagram showing the interference of polarized o-ray and e-ray
图15-59 偏振O射线和E射线的干涉示意图

Some substances, such as glass, celluloid and various plastics, with no natural doubly refracting, may become of double refracting ones when subjected to mechanical stress. From a study of the interference pattern due to the specimen between crossed polarized filters, much information regarding the stresses can be obtained.
某些物质，如玻璃、赛璐珞和各种塑料，没有自然的双重折射，在受到机械应力时可能会变成双折射。通过对交叉偏振滤光片之间样品引起的干涉模式的研究，可以获得有关应力的大量信息。

Improperly annealed glass, for example, may be internally stressed to an extent, which might cause it later to develop cracks. It is evidently important that optical glass should be free from such a condition before it is subjected to expensive grinding and polishing. Hence such glass is always examined by use of two crossed polarized filters before grind-
例如，退火不当的玻璃可能会在一定程度上受到内部应力，这可能会导致其以后出现裂纹。显然，光学玻璃在进行昂贵的研磨和抛光之前应该没有这种情况，这一点很重要。因此，在研磨之前，总是使用两个交叉的偏振滤光片来检查这种玻璃。
ing operations begin. ing 操作开始。

The tece double refraction produced by stress is the basis of neering ique of photo-elasticity. The stresses in opaque engi-
应力产生的双折射是光弹性的基础。不透明工程中的应力

Fig. 15-60 A photo-elastic stress pattern ling a materials, such as grinders, boilerplates, gear teeth etc., can be analyzed by construcject will be sparent model of the object, usually of a plastic. The transparent model of the obplaced between a polarizer and an analyzer which are in the crossed position and the
图15-60 光弹性应力图案 ling 一种材料，如磨床、样板、齿轮齿等，可以通过结构来分析物体的母体模型，通常是塑料。偏振片和分析仪之间的透明模型，它们处于交叉位置和
interference pattern of the model will be obtained. The stress distribution inside the object can be calculated by analyzing the interference pattern. Very complicated stress distributions, such as those around a hole or a gear tooth, which would be practically impossible to analyze mathematically, may thus be studied by optical methods. Usually, the denser the fringes are, the higher the stress is. Fig. 15-60 shows a model under light and heavy stress.
将获得模型的干涉图案。物体内部的应力分布可以通过分析干涉图案来计算。因此，可以通过光学方法研究非常复杂的应力分布，例如孔或齿轮齿周围的应力分布，这些应力分布实际上不可能通过数学分析。通常，条纹越密集，应力越大。图15-60显示了轻应力和重应力下的模型。

15-1 What type of experimental evidence indicates that light is a wave?
15-1 什么类型的实验证据表明光是波？

15-2 Light has wave characteristics in various media as well as in a vacuum. The wavelength of light is smaller in any medium than it is in a vacuum. Does the color change when light going from one medium to another? Why?
15-2 光在各种介质和真空中具有波动特性。光在任何介质中的波长都比在真空中小。当光线从一种介质转移到另一种介质时，颜色会发生变化吗？为什么？

15-3 Why are interference effects not more commonly observed? How do you get coherent light rays? Explain your methods.
15-3 为什么干扰效应不常见？你如何获得相干光线？解释你的方法。

15-4 Why does sound bend around the corner of a building while light does not?
15-4 为什么声音在建筑物的拐角处弯曲，而光线却没有？

15-5 Suppose the Young's double-slit experiment is performed with a glass plate with index of refraction covering the entrance to one of the slits. Describe the effect of this plate on the resulting pattern on the screen.
15-5 假设杨氏双缝实验是用一块玻璃板进行的，其折射率 覆盖了其中一个狭缝的入口。描述此板对屏幕上生成的图案的影响。

15-6 Suppose we perform the double-slit experiment under water. How would the pattern be affected?
15-6 假设我们在水下进行双缝实验。该模式将受到什么影响？

15-7 Imagine observing the double-slit pattern for light of a given wavelength and gradually reducing the slit spacing . What happens to the pattern? Is there a minimum spacing for observing a pattern? If so, what is this spacing?
15-7 想象一下，观察给定波长的光的双缝图案，并逐渐减小狭缝间距 。模式会发生什么变化？观察模式是否有最小间距？如果是这样，这个间距是多少？

15-8 When light rays in air encounter the surface of water or glass, is there phase reversed upon reflection?
15-8 当空气中的光线遇到水或玻璃表面时，反射时是否有相位反转？

15-9 A soap film on a wire loop held in air appears dark at its thinnest portion when viewed by reflected light. On the other hand, a thin oil film floating on water appears bright at its thinnest portion when similarly viewed from the air above. Explain this phenomenon.
15-9 在空气中固定的金属丝环上的肥皂膜在反射光下最薄的部分看起来很暗。另一方面，漂浮在水面上的薄油膜在从上方的空气中看时，其最薄的部分看起来很亮。解释这种现象。

15-10 Describe how the Newton's ring pattern would change if the lens radius was doubled; if the incident wavelength were doubled; if both the lens radius and wavelength were doubled.
15-10 描述如果透镜半径加倍，牛顿环图案将如何变化;如果入射波长加倍;如果镜头半径和波长都加倍。

15-11 If the Newton's ring arrangement was composed by three
15-11 如果牛顿环排列由三个组成

Fig. 15-61 For problem 15-11 transparent materials (Fig. 15-61) whose index of refraction are not the same. What is the shape of Newton's ring? Is the point bright or dark?
图15-61 对于问题15-11，折射率不相同的透明材料（图15-61）。牛顿环的形状是什么？点 是亮的还是暗的？

15-12 Describe the effect on the Fraunhofer diffraction pattern produced by a single slit if (1) the slit width is doubled; (2) the wavelength is doubled; (3) both the slit width and wavelength are doubled.
15-12 描述如果 （1） 狭缝宽度增加一倍;（2）波长加倍;（3）狭缝宽度和波长均加倍。

15-13 What is the purpose of a diffraction grating? Why does a grating have a large number of slits? Why are the slits of a grating spaced very close together?
15-13 衍射光栅的用途是什么？为什么光栅有大量的狭缝？为什么光栅的狭缝间隔得很近？

15-14 We can observe diffraction pattern when a monochromatic beam incident normally to a single-slit of a diffraction grating. Why the equations for bright fringes are different in above two arrangements? Bragg's law, , is closely related to the grating equation . Explain the origin of
15-14 当单色光束通常入射到衍射光栅的单缝时，我们可以观察到衍射图案。为什么上述两种排列中明亮条纹的方程不同？ 布拉格定律 与光栅方程密切相关 。解释的起源
the factor 2 in Bragg's law.
布拉格定律中的因子 2。

15-16 Unpolarized light falls on two polarizing filters so oriented that no light is transmitted. If the third polarizing filter is placed between them, can light be transmitted?
15-16 非偏振光落在两个偏振滤光片上，定向如此定向，不会透射光。如果在它们之间放置第三个偏振滤光片，可以透射光吗？

15-17 Devise a way to identify the polarizing direction of a filter of Polaroid without the help of another polarizing filter.
15-17 设计一种方法来识别宝丽来滤光片的偏振方向，而无需另一个偏振滤光片的帮助。

Maxwell's electromagnetic theory, made a great success in classical physics, led to new question about the propagation of light. Through what medium are the electromagnetic waves propagated? There was no obvious medium to which one could assign electromagnetic waves, since they were known to pass through a vacuum. However, most of physicists believed that some medium was necessary for energy to be transmitted through a distance, and this medium was given the name "ether". Does such as ether exist? If it exists, how can one detect it and determine its characteristics?
麦克斯韦的电磁理论在经典物理学中取得了巨大成功，引发了关于光传播的新问题。电磁波通过什么介质传播？没有明显的介质可以分配电磁波，因为已知它们会穿过真空。然而，大多数物理学家认为，能量通过远距离传输需要某种介质，这种介质被命名为“以太”。这样的以太存在吗？如果它存在，如何检测它并确定其特征？

If ether exists, the speed of light measured in a reference frame at rest with respect to this ether, according to the classical mechanics, should be different from the speed determined in a reference moving with respect to the ether. Thus the ether should provide an absolute reference frame to which the motions of all other frames and of all bodies in the universe could be referred. Then, how fast does the earth move relative to the ether ?
如果以太存在，根据经典力学，在静止的参考系中测量的相对于该以太的光速应该不同于相对于以太移动的参考中确定的速度。因此，以太应该提供一个绝对的参考系，所有其他系和宇宙中所有物体的运动都可以参考。那么，地球相对于以太的运动速度有多快呢？

Maxwell's theory told us that the speed of light in vacuum, given by
麦克斯韦的理论告诉我们，真空中的光速，由下式给出

is constant, independent of the reference frame. According to Galilean transformation of velocities, the speed of light in a reference frame is not equal to the speed in others. This means that Maxwell's theory is proper in a particular reference frame: ether. If so, we must find the ether. If we cannot detect the ether, what is the next step?
是常数，与参考系无关。根据伽利略速度变换，参考系中的光速不等于其他系中的速度。这意味着麦克斯韦的理论在一个特定的参考系中是正确的：以太。如果是这样，我们必须找到以太。如果我们无法检测到以太，下一步是什么？

In 1905, Einstein proposed a theory called the Special relativity. He abandoned the idea of the ether and insisted that there was not any absolute reference frame and all the inertial frames are equivalent with respect to all the physical laws. One principal focus of relativity has to do with measurements of events (things that happen): where and when they happen, and by how much any two events are separated in space and time. In addition, relativity has to do with transforming such measurements and others between reference frames that move relative to each other. This chapter introduces the Lorentz transformation, some of the consequences of the relativity and the famous mass-energy formula.
1905年，爱因斯坦提出了一个叫做狭义相对论的理论。他放弃了以太的概念，并坚持认为没有任何绝对的参考系，所有的惯性系相对于所有的物理定律都是等价的。相对论的一个主要焦点与事件（发生的事情）的测量有关：它们发生的地点和时间，以及任何两个事件在空间和时间上的间隔程度。此外，相对论还涉及在相对移动的参考系之间转换此类测量值和其他测量值。本章介绍了洛伦兹变换、相对论的一些结果和著名的质能公式。

In previous chapter, we have described the Michelson's interferometer. This section is devoted to an application of Michelson's interferometer in which the effects of ether (if it ex-
在上一章中，我们已经描述了迈克尔逊干涉仪。本节专门介绍迈克尔逊干涉仪的应用，其中以太的影响（如果它不包括
ists) on the earth is measured. Historically, Einstein may have known only vaguely of the Michelson-Morley result. He was concerned instead with problems in the electrodynamics of moving bodies-the appearance of the fields in a light wave to an observer moving at speed . However, the result of this experiment is helpful for one to abandon the idea of ether and to verify the relativity.
ists）在地球上被测量。从历史上看，爱因斯坦可能只模糊地知道迈克尔逊-莫雷的结果。相反，他关心的是运动物体的电动力学问题——光波中场对快速 移动的观察者的出现。然而，这个实验的结果有助于人们放弃以太的想法并验证相对论。

As shown in Fig. 16-1, a beam of light emitted by S is split into two parts by G. The light (1) goes from to mirror and then to and recombines with the light (2) which goes from to mirror and then to at . Assume that the earth is moving with velocity relative to the ether in the direction . That is the apparatus is moving in the ether.
如图16-1所示，S发出的一束光被G分成两部分。光 （1） 从 镜像到镜 像，然后到 并与光 （2） 重新组合，光 （2） 从 镜像 到镜像，然后到 。 假设地球 以相对于以太的速度在方向 上运动。也就是说，设备在以太中移动。

Fig. 16-1 Schematics of Michelson -Morley Experiment
图16-1 迈克尔逊-莫雷实验示意图

Given , we first consider the transit time of a light beam (1) moving perpendicular to the velocity of the apparatus relative to the ether The speed of light relative to the ether is c. According to Galilean transformation of velocity, the speed of light (1) relative to the earth is given by
给定 ，我们首先考虑光束 （1） 的传播时间，该光束垂直于设备相对于以太的速度移动，光相对于以太的速度为 c。根据伽利略速度变换， 光速 （1） 相对于地球由下式给出

The time required for the light (1) to go from to and then return to is equal to
光 （1） 从 到 然后返回 所需的时间 等于

In the same way, we obtain the time required for the light (2) parallel to to travel from to and then return to
以同样的方式，我们获得平行于 的 光 （2） 从 到 然后 返回 所需的 时间