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Single Slit Diffraction

# Single Slit Diffraction - Clearly the central maximum is...

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Single Slit Diffraction r is the distance from a point on the slit to P and can be approximated by r L - x sin θ . We can now perform the integration to find the electric field at P : E = sin[ σt - k ( L - x sin θ )] dx So: E = sin( σt - kL ) The irradiance is the time average of the electric field squared so recalling that the average of sin 2 ( σt ) we find that: I = which is the same as the result above if we recall k = . It also follows from this calculation that the maxima occur not half way between the minima as might be expected but at the points correponding to the solution of the transcendental equation: tan( Πd / λ ) = Πd / λ These are at ±1.4303 Π , ±2.4590 Π , ±3.4707 Π , etc. A plot of irradiance versus position is shown in .

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Figure %: Intensity as a function of position for the single slit.
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Unformatted text preview: Clearly the central maximum is much brighter than any of the surrounding maxima, due to the partial cancellation that occurs. The analysis by integration over the slits can easily be extended to double or multiple slit systems, or even rectangular or circular apertures. In the double slit case, the diffraction pattern resembles the double slit interference pattern we found for Young's experiment , modulated by the envelope of a diffraction pattern similar to the single slit. Figure %: Double slit interference and diffraction pattern. As the size of the slits goes to zero, the pattern assumes the form shown in ....
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