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الكلية كلية العلوم للبنات
القسم قسم فيزياء الليزر
المرحلة 2
أستاذ المادة محمد حمزة خضير المعموري
27/09/2019 16:47:20
reflecting material such that the reflected ray makes the same angle with the normal as the incident ray. If the reflecting surface is a boundary between two different transparent mediums, such as air and glass, some of the incident light is also transmitted into the glass, as shown in figure 31.1. However, it is observed Figure 31.1 Reflection and refraction of light. experimentally that this transmitted ray of light is bent as it enters the second medium. The bending of light as it passes from one medium into another is called refraction. Refraction of light occurs because light travels at different speeds in different mediums. Light traveling through a vacuum travels at the speed c = 3.00 × 108 m/s. But when light enters a medium there is a complex interaction between the electromagnetic wave (light) and the atomic configuration of the medium. This interaction causes the electromagnetic wave to slow down in the medium. This slowing down of the wave as it goes from a vacuum into the medium causes it to bend. We will use Huygens’ principle to show how this is accomplished in section 31.2. 311 31.2 The Law of Refraction Let us consider a wave front B1B2 of a plane parallel monochromatic wave impinging on the boundary of two different mediums, as shown in figure 31.2. The incident ray makes an angle of incidence i with the normal N. The incident light Figure 31.2 The law of refraction by Huygens’ principle. moves at a speed v1 in medium 1 and v2 in medium 2, and we assume that v1 is greater than v2. The incident wave has just touched the boundary at B1. In a time ?t, B2, the upper portion of the initial wave front, travels a distance v1?t, and impinges at the boundary of the interface at B’2. In this same time interval ?t, the wave front at B1 enters the second medium. By Huygens’ principle, a secondary wavelet can be drawn emanating from the point B1. This wave moves a radial distance v2?t in the second medium in the time interval ?t, and is shown as the circle of radius v2?t in the figure. The radial distance v2?t is less than the distance v1?t because v2 is less than v1. By Huygens’ principle, the line drawn from B’2 that is tangent to the secondary wavelet is the new wave front. The point of tangency is denoted by B’1 and the new wave front in medium 2 is B’1B’2 .The radius from B1 to B’1, when extended, becomes the refracted ray B1C. The other refracted rays are drawn parallel to B1C, as shown in figure 31.2. The angle that the refracted ray makes with the normal is called the angle of refraction r. We can obtain the relation between the angles i and r from the geometry of figure 31.2. Since line B2B’2 makes an angle i with the dashed normal, angle B2B’2B1 is equal to (900 ? i), and since the sum of the angles in triangle B1B2B’2 must equal 1800, it follows that angle B2B1B’2 is also equal to the angle i. Using similar reasoning, angle B1B’2B’1 is equal to r. Hence, from the trigonometry of figure 31.2, Chapter 31 The Law of Refraction 312 sin i = v1?t (31.1) B1B’2 and sin r = v2?t (31.2) B1B’2 Let us divide equation 31.1 by equation 31.2 and obtain sin i sin r = v1?t B1B2 ? v2?t B1B2 ? and sini (31.3) sin r = v1 v2 = constant = n21 Equation 31.3 is the law of refraction. It says that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speed of light in medium 1 to the speed of light in medium 2. Because the speed of light in medium 1 v1 is a constant and the speed of light in medium 2 v2 is a constant, then their ratio v1/v2, must also be a constant. This constant is called the index of refraction of medium 2 with respect to medium 1 and is denoted by n21. If medium 1 is a vacuum, then v1 = c, and the index of refraction of the medium with respect to a vacuum is n = c (31.4) v Since the speed v in any medium is always less than c, the index of refraction, n = c/v, is always greater than 1, except for in a vacuum where it is equal to 1. Indices of refraction for various substances are given in table 31.1. Notice that the index of refraction of air is so close to the value 1, the index of refraction of a vacuum, that in many practical situations, air is used in place of a vacuum. The law of refraction can be put in a more convenient form by using equation 31.4. We can write the index of refraction of medium 1 with respect to a vacuum as n1 = c (31.5) v1 whereas we can write the index of refraction of medium 2 with respect to a vacuum as n2 = c (31.6) v2 Chapter 31 The Law of Refraction 313 1.00029 1.5 2.42 1.52 1.571.72 1.46 1.47 1.31 1.49 1.54 1.33 Air Benzene Diamond Glass, crown Glass, flint Glass, fused quartz Glycerine Ice Plexiglass Quartz crystal Water Substance n Table 31.1 Index of Refraction for Various Materials (? = 589.2 nm, the D line of sodium) Solving for the speeds v1 and v2 from equations 31.5 and 31.6, respectively, and substituting them into equation 31.3, gives n21 = v1 = c/n1 = n2 (31.7) v2 c/n2 n1 Using equation 31.7, we can write the law of refraction, equation 31.3, as sin i = n21 = n2 sin r n1 or n1 sin i = n2 sin r (31.8) Equation 31.8 is the form of the law of refraction that we will use in what follows. It is also called Snell’s law after its discoverer, Willebrord Snell (15911626) a Dutch mathematician who discovered it in 1620, the same year the Pilgrims landed at Plymouth Rock. Note that if a ray lies along the normal, then the angle of incidence i is equal to zero, and hence the angle of refraction r must also be zero, and there is no refraction of this ray. The fact that the speed of light varies from medium to medium has an important effect on the wavelength of light. When an initial wave enters a second medium, its wavelength changes. We can see this from equation 31.3, w
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