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happyphysics.com Physics Lecture Resources Prof. Mineesh Gulati Head-Physics Wing Happy Model Hr. Sec. School, Udhampur, J&K Website: happyphysics.com

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Ch 35 Interference © 2005 Pearson Education

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35.1 Interference and Coherent Sources The principle of superposition: When two or more waves overlap, the resultant displacement at any point and at any instant is found by adding the instantaneous displacements that would be produced at the point by the individual waves if each were present alone. © 2005 Pearson Education

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Sinusoidal wave spreading out from 2 coherent source

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© 2005 Pearson Education Constructive interference Destructive interference

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© 2005 Pearson Education Antinodal curves

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35.2 Two-Source Interference of Light © 2005 Pearson Education

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Path length difference

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© 2005 Pearson Education

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constructive interference, two slits destructive interference, two slits constructive interference in Young’s experiment © 2005 Pearson Education

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35.3 Intensity in interference Patterns © 2005 Pearson Education Phasor diagram for superposition

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amplitude in two-source interference intensity in two-source interference phase difference related to path difference © 2005 Pearson Education

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Intensity distribution in interference pattern from 2 identical slits

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35.4 Interference in Thin Films © 2005 Pearson Education

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constructive reflection from thin film, no relative phase shift destructive reflection from thin film, no relative phase shift

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© 2005 Pearson Education

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35.5 The Michelson Interferometer © 2005 Pearson Education

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Monochromatic light is light with a single frequency. Coherence is a definite, unchanging phase relationship between two waves. The overlap of waves from two coherent sources of monochrowave disturbance at any point is the sum of the disturbances from the separate waves.

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When two sources are in phase, constructive interference occurs at points where the difference in path length from the two sources is zero or an integer number of wavelengths; destructive interference occurs at points where the path difference is a half- integer number of wavelengths. If two sources separated by a distance d are both very far from a point P, and the line from the sources to P makes an angle θ with the line perpendicular to the line of the sources, then the condition for constructive interference at P is Eq. (35.4). The condition for destructive interference is Eq. (35.5). When θ is very small, the position y m of the mth bright fringe on a screen located a distance R from the sources is given by Eq. (35.6). (See Examples 35.1 and 35.2) © 2005 Pearson Education

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When two sinusoidal waves with equal amplitude E and phase difference φ are in superimposed, the resultant amplitude E p and intensity I are given by Eqs. (35.7) and (35.10) respectively. If the two sources emit in phase, the phase difference φ at a point P (located a distance r1 from source 1 and a distance r2 from source 2) is directly proportional to the difference in path length r2- r1.(See Example 35.3) © 2005 Pearson Education

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When light is reflected from both sides of a thin film of thickness t and no phase shift occurs at either surface, constructive interference between the reflected waves occurs when 2t is equal to an integral number of wavelengths. If a half-cycle phase shift occurs at one surface, this is the condition for destructive interference. A half-cycle phase shift occurs during reflection whenever the index of refraction in the second material is greater than that in the first. (See Examples 35.4 through 35.8) © 2005 Pearson Education

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The Michelson interferometer uses a monochromatic light source and can be used for high-precision measurements of wavelengths. Its original purpose was to detect motion of the earth relative to a hypothetical ether, the supposed medium for electromagnetic waves. The ether has never been detected, and the concept has been abandoned; the speed of light is the same relative to all observers. This is part of the foundation of the special theory of relativity. © 2005 Pearson Education

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