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Topics. Slit width and slit separation dependence of diffraction pattern for single and double slits in the Fraunhofer (far-field) regime. Babinet’s principle: Determine the thickness of your hair. Diffraction pattern for circular apertures.

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  1. Topics • Slit width and slit separation dependence of diffraction pattern for single and double slits in the Fraunhofer (far-field) regime. • Babinet’s principle: Determine the thickness of your hair. • Diffraction pattern for circular apertures. • Quantitatively measuring the intensity distribution of the diffraction patterns of single and double slits in the Fraunhofer (far-field) regime and fitting data to theory. • Determination of the ration of slit-width a and slit separation-distance d from the double slit diffraction pattern.

  2. VII.A Experiments with the Observation Screen • Look at single slit diffraction pattern for different slit widths. • Determine the laser wavelength from the diffraction pattern minima from a single slit. x Q I(x) L

  3. Babinet’s Principle The diffraction pattern in the far field due to a given screen is the same as the diffraction pattern due to it’s complement. Translation for our experiment: A slit of width a produces the same diffraction pattern as a hair of the same width. x Q I(x) L

  4. VII.A Determine the Thickness of your Hair Tape hair to component holder View from the front Laser beam should hit the hair

  5. VII.A Diffraction pattern of a small circular aperture View from the front Use the slide that contains circular apertures of sizes 0.04mm and 0.08mm (those you should use). It also contains a big square and a big round hole with patterns inside.

  6. VII.A Diffraction pattern of a small circular aperture

  7. Mathematical Description of the Diffraction Pattern of a Circular Aperture in the Far-Field J1 = “Order One Bessel Function”

  8. Mathematical Description of the Diffraction Pattern of a Circular Aperture in the Far-Field

  9. Mathematical Description of the Diffraction Pattern of a Circular Aperture in the Far-Field

  10. VII.B Experiments with Linear Translator,……. • Observe the diffraction pattern intensities at your setup using the linear translator, photometer, and oscilloscope. • Record patterns using translator, photometer, noise filter, 750 interface, and Data Studio at the front table and email the results to yourself. • Process the measured intensity pattern with Excel and generate a theoretical intensity pattern in Excel. • Compare measured and theoretical pattern in a graph in Excel.

  11. VII.B Example of Processing Single Slit Data in Excel From Data Studio Calculate the theoretical Intensity distribution. Calculate from “Time”-column (Time-tc=0 at peak of pattern) Calculate from “Voltage”-column (so that Voltage-Voffset goes to zero at the edges of the pattern.

  12. VII.B Calculating I(t) You can read that off your data (Voltage-Voffset at the maximum intensity) D = distance from the slit to the fiber optic cable a = slit width l=632.8nm v = 10mm/min t = Time - Toffset

  13. VII.B Hints for getting the ratio of slit width a and slit separation d for the double slit from the diffraction pattern. Double slit maxima mdouble=1,2,3 Single slit minimum msingle=1

  14. Double slit maxima mdouble=1,2,3 Single slit minimum msingle=1

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