chapter27_1 - Chapter 27 Wave Optics Speed of Light in...

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Chapter 27 Wave Optics
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Speed of Light in Media ± Speed of light in media v, v=c/n, = speed of light in a vacuum n average speed of light in a medium c n v Index of refraction or refractive index •For a vacuum, n = 1 •(we assume n = 1 for air, also) •For other media, n > 1
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Indices of Refraction of Media
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Wavelength in Media ± As a wave travels from one medium to another, its frequency does not change. v 1 =c/n 1 =f λ 1 , v 2 =c/n 2 =f λ 2 Æ λ 1 n 1 = λ 2 n 2 = λ 0 λ n = λ 0 /n From vacuum (n=1) to a medium (n), wavelength is decreased by factor of n!
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Wave Fronts and Rays ± Wave front: surface connecting points of equal phase ± Ray: line perpendicular to the wave front For plane waves, wave fronts are geometric planes; rays are parallel lines
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Ray Approximation at a Barrier ± A wave meets a barrier with λ <<d ± d is the diameter of the opening ± The individual waves emerging from the opening continue to move in a straight line ± This is the assumption of the ray approximation ± Good for the study of mirrors, lenses, prisms, and associated optical instruments
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Ray Approximation at a Barrier ± The wave meets a barrier whose size of the opening is on the order of the wavelength, λ ~d ± The waves spread out from the opening in all directions ± The waves undergo diffraction
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Interference ± In constructive interference the amplitude of the resultant wave is greater than that of either individual wave ± In destructive interference the amplitude of the resultant wave is less than that of either individual wave
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Interference ± Condition for interference: ± The sources must be coherent ± They must maintain a constant phase with respect to each other ² All interference associated with light waves arises when the electromagnetic fields that constitute the individual waves combine
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Sources for Interference: Double- Slits ± Single light source from left (single wavelength) ± Two sources have the same wavelength ± Two sources are coherent: always in phase with each other
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Young’s Double Slit Experiment ± Thomas Young first demonstrated interference in light waves from two sources in 1801
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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
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Interference Patterns, 2 ± The lower wave has to travel farther than the upper wave to reach point P ± The lower wave travels one wavelength farther ± Therefore, the waves arrive in phase ± A second bright fringe occurs at this position Path length diff.= one wavelength or phase diff.= 2 π Constructive interference!
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Interference Patterns, 3 ± The lower wave travels one-half of a wavelength farther than the upper wave to reach
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This note was uploaded on 06/08/2009 for the course PHYS 2c taught by Professor All during the Spring '08 term at UC Riverside.

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chapter27_1 - Chapter 27 Wave Optics Speed of Light in...

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