Lecture 1202 Wave Optics Physics Help Q&A: tutor.leiacademy.org Total Internal Reflection A phenomenon called total internal reflectioncan occur when light is directed from a medium having a given index of refraction toward one having a lower index of refraction. 1
Possible Beam Directions Possible directions of the beam are indicated by rays numbered 1 through 5. The refracted rays are bent away from the normal since n 1 > n 2. Critical Angle There is a particular angle of incidence that will result in an angle of refraction of 90. This angle of incidence is called the critical angle, θ C. = > For angles of incidence greaterthan the critical angle, the beam is entirely reflected at the boundary. This ray obeys the law of reflection at the boundary. Total internal reflection occurs only when light is directed from a medium of a given index of refraction toward a medium of lower index of refraction. 2
Critical Angle, cont. For angles of incidence greaterthan the critical angle, the beam is entirely reflected at the boundary. This ray obeys the law of reflection at the boundary. Total internal reflection occurs only when light is directed from a medium of a given index of refraction toward a medium of lower index of refraction. Fiber Optics An application of internal reflection Plastic or glass rods are used to pipe light from one place to another. Applications include: Medical examination of internal organs Telecommunications 3
Construction of an Optical Fiber The transparent core is surrounded by cladding. The cladding has a lower nthan the core. This allows the light in the core to experience total internal reflection. The combination is surrounded by the jacket. Fiber Optics, cont. A flexible light pipe is called an optical fiber. A bundle of parallel fibers (shown) can be used to construct an optical transmission line. 4
Fiber Optics Example Assume a transparent rod of diameter d = 4.83 μmhas an index of refraction of 1.37. Determine the maximum angle θ for which the light rays incident on the end of the rod in the figure below are subject to total internal reflection along the walls of the rod. Your answer defines the size of the cone of acceptance for the rod. = 1 = 1.37 Fiber Optics Example Find = 1 = 90 = 1.37 = = + = 90 = 1 1.37 = 46.88 = 43.12 = = 0.936 = 69.46 5
Wave Optics Wave optics is a study concerned with phenomena that cannot be adequately explained by geometric (ray) optics. Sometimes called physical optics These phenomena include: Interference Diffraction Polarization Young s Double-Slit Experiment Thomas Young first demonstrated interference in light waves from two sources in 1801. The narrow slits S 1 and S 2 act as sources of waves. The waves emerging from the slits originate from the same wave front and therefore are always in phase. 6
Resulting Interference Pattern The light from the two slits forms a visible pattern on a screen. The pattern consists of a series of bright and dark parallel bands called fringes. Constructive interferenceoccurs where a bright fringe occurs. Destructive interferenceresults in a dark fringe. Conditions for Interference To observe a stable interference pattern in light waves from two or more sources, the following two conditions must be met: The sources must be coherent. They must maintain a constant phase or phase difference between each other. The sources should be monochromatic. Monochromatic means they have a single wavelength and frequency. Waves of different frequency still interfere but they won t form a stable bright-dark pattern. 7
Producing Coherent Sources Light from a monochromatic source is often used to first illuminate a single slit. The wave from the single slit is conditioned in shape, uniformity, and coherence. This light is then used to illuminate the double-slit to produce interference patterns. In modern days, Laser is often used to directly illuminate the double-slit to produce interference patterns. The light from a Laser is coherent and monochromatic. Light Passing through Narrow Slits If the light traveled in a straight line after passing through the slits, no interference pattern would be observed. From Huygens s principle we know the waves spread out from the slits. This divergence of light from its initial line of travel is called diffraction. 8
Interference Patterns Constructive interference occurs at point O. The two waves travel the same distance. Therefore, they arrive in phase As a result, constructive interference occurs at this point and a bright fringe is observed. 9
Interference Patterns The lower wave travels farther than the upper wave to reach point P. If the lower wave travels one wavelength farther than the upper wave, when the two waves meet at P, they will be in phase. In this case, constructive interference occurs and a bright fringe occurs at this position. This also happens when the path difference of the two waves are integer multiples of the wavelength. = ± = 0,1,2, Interference Patterns At point R, suppose the path difference is one half wavelength ( /2). That is, the lower wave travels /2more than the upper wave. This path difference will cause the two waves be out of phase with a phase difference of $. In this case, destructive interference occurs and a dark fringe will be observed. This also happens when the path difference of the two waves are odd integer multiples of one half wavelength. = ± + 1 2 = 0,1,2, 10
Analysis of Double-Slit Experiment: Geometry The interference is determined by the phase difference of the two waves from the two slits, and the phase difference is determined by the path difference. The key point here is to find the path difference, %. For geometry of the experiment set up, it is assumed that & (. Therefore, and are almost parallel. With this approximation, the path difference can be found as: % = = ( This assumes the paths are parallel. Not exactly true, but a very good approximation if Lis much greater than d Interference Equations For a bright fringe produced by constructive interference, the path difference must be either zero or some integer multiple of the wavelength. % = ( )*+,-. = ± = 0,1,2, m is the order number m = 0 gives the zeroth-order maximum m = 1 corresponds to two the first-order maxima When destructive interference occurs, a dark fringe is observed. This needs a path difference of an odd multiple of one half wavelength. = % ( 23 = 4 & % = ( /0*1 = ± + 1 2 = 0,1,2, 11
Interference Equations When & (, and (, we can use the small angle approximation: = 23 4 = & % ( y-position of the fringes: % ( = 4 & = % ( 23 = 4 & 4 )*+,-. = ±& ( % = ( )*+,-. = ± = 0,1,2, 4 /0*1 = ±& (+1 2 ) ( % = ( /0*1 = ± + 1 2 = 0,1,2, Applications of Young s Double-Slit Experiment Young s double-slit experiment provides a method for measuring wavelength of the light. This experiment gave the wave model of light a great deal of credibility. It was inconceivable that particles of light could cancel each other in a way that would explain the dark fringes. 12
13
14