Modern Optics Lab Lab 7: Diffraction and Interference Experiments  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. Topics

Modern Optics Lab Lab 7: Diffraction and Interference Experiments 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 I(x)  L

Modern Optics Lab Lab 7: Diffraction and Interference Experiments 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 I(x)  L

Modern Optics Lab Lab 7: Diffraction and Interference Experiments VII.A Determine the Thickness of your Hair View from the front Tape hair to component holder Laser beam should hit the hair

Modern Optics Lab Lab 7: Diffraction and Interference Experiments 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.

Modern Optics Lab Lab 7: Diffraction and Interference Experiments VII.A Diffraction pattern of a small circular aperture

Modern Optics Lab Lab 7: Diffraction and Interference Experiments Mathematical Description of the Diffraction Pattern of a Circular Aperture in the Far-Field J 1 = “Order One Bessel Function”

Modern Optics Lab Lab 7: Diffraction and Interference Experiments Mathematical Description of the Diffraction Pattern of a Circular Aperture in the Far-Field

Modern Optics Lab Lab 7: Diffraction and Interference Experiments

Modern Optics Lab Lab 7: Diffraction and Interference Experiments Mathematical Description of the Diffraction Pattern of a Circular Aperture in the Far-Field

Modern Optics Lab Lab 7: Diffraction and Interference Experiments 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 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.

Modern Optics Lab Lab 7: Diffraction and Interference Experiments VII.B Example of Processing Single Slit Data in Excel TimeVoltageTime-t c Voltage-V offset I(t) ….. …… From Data Studio Calculate from “Time”-column (Time-tc=0 at peak of pattern) Calculate from “Voltage”-column (so that Voltage-V offset goes to zero at the edges of the pattern. Calculate the theoretical Intensity distribution.

Modern Optics Lab Lab 7: Diffraction and Interference Experiments VII.B Calculating I(t) You can read that off your data (Voltage-V offset at the maximum intensity) D = distance from the slit to the fiber optic cable a = slit width =632.8nm v = 10mm/min t = Time - T offset

Modern Optics Lab Lab 7: Diffraction and Interference Experiments 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 m double =1,2,3 Single slit minimum m single =1

Modern Optics Lab Lab 7: Diffraction and Interference Experiments Double slit maxima m double =1,2,3 Single slit minimum m single =1