L11_interference_diffraction4 - Single Slit Diffraction &...

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Single Slit Diffraction & Interference Theory - Diffraction When monochromatic, coherent light falls upon a small single slit it will produce a pattern of bright and dark fringes. These fringes are due to light from one side of the slit interacting (interfering) with light from the other side. The positions of the minima (destructive interference – appears dark because of a lack of light) for a single slit are given by the equation m = a sin m where is the wavelength of the light, a is the width of the slit, is the angle between the central axis of the slit and maximum, and m is an integer = 0, 1, 2, 3, . ... For a large L (L>>y), we can approximate sin m by y m /L. Thus, our equation for the minima becomes m = a (y m /L) Note that we can find the width of the central maximum through: y o = (y 1 - y -1 ) = (L(1) )/a - (L(-1) )/a = 2(L )/a For the width of the first maximum and the following maxima: y 1 = (y 2 - y 1 ) = (L(2) )/a - (L(1) )/a = (L )/a y 2 = (y 3 - y 2 ) = (L(3) )/a - (L(2) )/a = (L )/a = y 1 The following Figure shows a pattern similar to what we see in a lab setting. Labels pinpoint the pattern features. Theory - Interference A similar pattern appears when we combine light from two identical source. Since it is practically impossible to obtain two light sources that are identical, we obtain the same effect by shining light from a laser on two closely spaced slits. Each of the slits acts then as a source. We use a laser because the light produced by a laser is monochromatic and coherent. Shining light on the two slits results in a static pattern of constructive and destructive interference fringes like the one shown in Figure 3. These can be projected on a screen behind the slits and appear as bright and dark fringes called maxima and minima. The positions of constructive, bright, interference fringes are given by: m = d sin m where is the wavelength of the light, d is the separation of the slits, m is the angle between the central axis of the slit and the m-th position of constructive interference, and m is an integer = 0, 1, 2, 3, . ... y m m = 0 m = 1 m = 2 m = 3 m = 4 m = -1 m = -2 m = -3 m = -4 Laser m L d Fig. 3: Diagram of variables in double slit experiment m = 1 y m Laser m L a m = 2 m = -2 m = -1 Fig. 1: Diagram of a single slit experiment
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While this looks very much like the equation that we use for single slit diffraction, it should be noted that this equation refers to maxima, and not minima. If we restrict ourselves to only consider those maxima that are close to the central maximum, then the angle
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This note was uploaded on 02/09/2011 for the course PHYS 1112L taught by Professor Adler during the Summer '10 term at Kennesaw.

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L11_interference_diffraction4 - Single Slit Diffraction &...

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