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الكلية كلية العلوم للبنات
القسم قسم فيزياء الليزر
المرحلة 2
أستاذ المادة محمد حمزة خضير المعموري
27/09/2019 16:36:12
INTRODUCTION It has been shown that electromagnetic waves in matter travel at a speed that is reduced, and can be expressed in terms of the refractive index n: ? = ? ? where Maxwell’s equations were used to predict that the refractive index ? is given by: ? = ??? ?? For nonferromagnetic materials the relative permeability is very close to unity and then ? = ??? where ?? is the dielectric constant. The plane EM wave in matter has the relation between the perpendicular coupled electromagnetic fields ? = ?? and travels in the ??E × ??B direction. In the absence of any obstructions or media effects, electromagnetic radiation travels in straight lines. The fact that light travels in straight lines, and casts a sharp shadow, led Newton to believe that light involved particle motion not wave motion. Solutions of the wave equation also predict electromagnetic waves traveling in a straight line. For example, we saw that a plane wave of the form ??E = ?0bi sin(?? ? ??) travels in the ? direction. However, last lecture it was shown that waves behave differently when obstructions are encountered. The difference between particle and wave motion is that, for obstructions comparable in size to the wavelength, waves are diffracted outwards at the edges. The angle of the first minimum for diffraction at a slit of width d is given by sin ? = ? ? . Diffraction effects become negligible when ? ?? ?, which is the realm of geometric optics. For many applications of wave propagation, such as optics, diffraction effects can be ignored, to first order, allowing use of geometrical optics, the topic of today’s lecture. Although the propagation of waves can be predicted exactly using mathematical solutions of the wave equation, with known boundary conditions, you may Figure 1 Huygens construction for propagation to the right of (?) a plane wave, and (?) an outgoing spherical wave. find it helpful to consider the Huygens construct of secondary wavelets to explain wave motion. The Huygens construct assumes that each point on a primary wavefront serves as the source of spherical secondary wavelets that advance with the speed and frequency of the primary wavefront. Figure 1 illustrates the Huygens construct for the propagation of plane and spherical waves. The secondary wavefront is the locus of the secondary wavelets. Note that the wavelets do spread outwards into the shadow at the edge of the plane wave. Calculation of the secondary wavefront requires including the relative phases and amplitudes of the wavelets involved. The Huygens construct is useful in understanding reflection, refraction and diffraction. The trajectory taken by an electromagnetic wave also is predicted by Fermat’s principle which states that the wavefront follows a path that minimizes the transit time. REFLECTION AND REFRACTION AT BOUNDARIES The reflection and transmission of electromagnetic waves incident normally at the boundary between two media has been discussed and the reflectivity and transmission calculated. When waves are incident upon a boundary at nonnormal incidence, the reflected and transmitted waves are emitted at definite nonnormal angles, and the reflectivity and transmission differ from the case of normal incidence discussed earlier. The angles of incidence, reflection and refraction are most conveniently measured with respect to the normal to the boundary surface. The plane of incidence is the surface defined by the incident ray and the normal to the surface. 133 Figure 2 Wave with velocity v1in medium 1 incident upon a boundary with medium 2 in which the wave has velocity v2? The angle of incidence to the normal to the surface is ??? the angle of reflection to the normal is ??, and the angle of refraction relative to the normal is ?? ? Reflection Reflected and incident waves are in the same material and therefore have the same velocity. Therefore, using the Huygens construct shown in figure 2, it can be seen that the reflected wave is in the plane of incidence and the angle of reflection equals the angle of incidence. ?? = ?? Refraction The transmitted wave travels in a different medium, with different speed compared to the incident wave. Using the Huygens construct, one can see that in a given time ??? the incident and transmitted waves travel the distances ???? and ?? ?? respectively. Since the two wavefronts have a common hypotenuse, then we have the relation that gives the angle of refraction of the transmitted wave: sin ?? sin ?? = ?? ? ??? that is: sin ?? ?? = sin ?? ?? These two relations for the angles of reflection and refraction are true for any type of travelling wave. For electromagnetic waves, the velocity can be expressed in terms of the refractive index, that is ? = ? ? ? Using this, leads to Snell’s Law that gives the refracted wave is in the plane of incidence at an angle of refraction given by: ?? sin ?? = ?? sin ?? (Snell’s Law) As an example, consider light in air incident upon glass of refractive index ? = 1?5 as shown in figure Figure 3 Refraction of light by airglass interface. Figure 4 Total internal reflection when n1 ? ?2? 3. For normal incidence ?? = ?? = ?? = 0? For an incident angle ?? = 45?, the angle of reflection is 45? and the angle of refraction is given by: sin ?? = 1 1?5 sin 45? which gives ?? = 28?13?? At the maximum angle of incidence ?? = 90?, then Snell’s law gives ?? = 41?81?? Critical angle When electromagnetic radiation strikes a boundary going from higher to lower refractive index, the transmitted wave is bent away from the normal at a larger angle than the angle of incidence as shown in figure 4. For incident angles at the critical angle, ??? the angle of refraction is 90?. That is, sin ?? = ?2 ?1 (Critical angle) For angles of incidence ?? ? ?? there is no solution to Snell’s law since there is no angle for which the sine exceeds unity. For angles of incidence greater than the critical angle, the incident wave is totally internally reflected, there is no transmitted wave. Thus the surface behaves as a perfect mirror. Underwater swimmers are familiar with this phenomenon, they can see upwards through only an angular region of the water surface within ? = 48?8? of the normal to can be totally internally reflected twice to exactly reverse the direction of travel using a rightangle prism. Four such prisms are used in binoculars to correct for inversion of the image by the lens. An important technical application of total internal reflection is the optical fiber illustrated in figure 6. This has applications in medicine as well as for longdistance transmission of signals. Polarization Since electromagnetic waves are transverse waves it can be shown that when the angle of reflection plus angle of refraction sum to 90?, the reflected wave is plane polarized as illustrated in figure 7. The reflected wave is fully plane polarized at the Brewster angle given by: tan ????????? = ?2 ?1 Polaroid sunglasses can be used to attenuate the polarized reflected light from a surface such as a window. REFLECTION AT SINGLE SURFACE Geometrical optics for reflective systems, that is when ? ?? ?, is dominated by the statement that the reflected wave is in the plane of incidence and the angle of reflection equals the angle of incidence. Let us consider simple reflective systems. Figure 7 Polarization of reflected light. Figure 8 Image formed by reflection from a plane mirror. Plane mirror As shown in figure 8, radiation reflected from the mirror appears to emanate from a virtual image that is the same distance behind the mirror as is the object in front of the mirror. An important feature of the mirror image is that depth inversion results in a righthanded system,bi ×bj = bk having a lefthanded mirror image wherebi ×bj = ?bk? This is illustrated in figure 9. The behaviour of physics under transformation of a righthanded system into a lefthanded mirrorimage system is an important fundamental symmetry of nature. Concave mirrors Consider the concave spherical surface of radius ? shown in figure 10? Let the object be a distance ? and image a distance ? from the mirror. From elementary Figure 9 Mirror image of a righthandthe surface. For gl
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
