Lecture27_Kim

Lecture27_Kim - Lecture 27-1 Diffraction Any wave passing...

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Lecture 27-1 Diffraction • Any wave passing through an opening that is about the same size as the wavelength of the wave ( ) will experience diffraction Example: water wave The same applies to light waves Diffraction: – The wave spreads out on the other side of the opening (rather than having the opening cast a sharp shadow), and – Develope interference pattern (called a diffraction pattern) • Light passing a sharp edge will also exhibit a diffraction pattern a 
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Lecture 27-2 Single Slit Diffraction: First Dark Fringe (1) To study the interference let’s expand and simplify our previous figure for single slit diffraction We assume coherent light with wavelength incident on a slit with width a that produces an interference pattern on a screen at distance L Just like in the double-slit experiment, we analyze pairs of light waves emitted from points in the slit
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Lecture 27-3 Single Slit Diffraction: First Dark Fringe (2) We start with light emitted from the top edge of the slit and from the center of the slit as shown To analyze the path difference we show an expanded version of our figure to the right Here we assume that the point P on the screen is far enough away that the rays r 1 and r 2 are parallel and make an angle with the central axis C
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Lecture 27-4 Single Slit Diffraction: First Dark Fringe (3) W e assume that the point P on the screen is far enough away that the rays r 1 and r 2 are parallel and make an angle with thecentral axis Therefore the path length difference for these two rays is The criterion for the first dark fringe is Although we chose one ray originating from the top edge of the slit and one from the middle of the slit to locate the first dark fringe, we could have used any two rays that originated a /2 apart inside the slit sin sin or / 2 2 xa x a   sin sin 22 a x or a   
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Lecture 27-5 Single Slit Diffraction: Second Dark Fringe (1) Now let’s consider four rays instead of two Here we choose a ray from the top edge of the slit and three more rays originating from points spaced a /4 apart
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Lecture 27-6 Single Slit Diffraction: Second Dark Fringe (2) The path length difference between the pairs of rays ( r 1 , r 2 ), ( r 2 , r 3 ), ( r 3 , r 4 ) is given by
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Lecture27_Kim - Lecture 27-1 Diffraction Any wave passing...

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