1. 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

2. 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

3. 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

4. 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

5. 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.

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

7. 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”

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

9. Modern Optics Lab Lab 7: Diffraction and Interference Experiments

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

11. 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 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.

12. 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) 01.1-25 11.1-24 21.1-23 31.2-22 ….. …… 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.

13. 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

14. 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

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