2054Lecture4 - The Principle of Superposition &...

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Unformatted text preview: The Principle of Superposition & Interference Superposition Principle of Superposition Principle When two or more waves occur When simultaneously at the same location, the resulting disturbance is the sum of all the individual disturbances. For example, the interaction of many waves which differ by a phase constant φ i is given by phase y ( x, t ) = ∑ i y m sin ( k i x − ω i t + φ i ) Types of Interference Types Constructive interference occurs when Constructive light from sources reinforce each other using the principle of linear superposition. using Destructive interference occurs when light from sources cancel each other using the principle of linear superposition. principle Constructive Interference Constructive Constructive interference occurs when the Constructive path difference d2-d1 is some integer multiple n of the wavelength λ , and is given by given d 2 − d 1 = nλ where n=0, 1, 2,…. where n=0, Destructive Interference Destructive Destructive interference occurs when the Destructive path difference d2-d1 is some half-integer multiple of the wavelength λ , and is given by by 1 d 2 − d1 = n + λ 2 where n = 0, 1, 2, 3,…. where 0, Diffraction Diffraction The bending of a wave around an obstacle or The the edges of an opening is called diffraction. For a single slit of width D or circular aperture of single circular diameter D, the first minimum of a wave of the wavelength λ is given by λ sin θ = D or λ sin θ = 1.22 D where θ is the angular spread of the wave, respectively. respectively. ...
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