REPORT FOR LAB F3: OPTICAL DIFFRACTION

Nathaniel Kan4/20/02

ABSTRACT:

In the Optical Diffraction lab we used an X-Y recorder to record the diffraction and interference patterns created by shining a laser through a variety of slit patterns, including a single slit, a double slit, multiple slits and a square slit.

PURPOSE:

The purpose of the Optical Diffraction lab was to investigate interference and diffraction patterns created by projecting a laser through various slit patterns. In our lab we used a single slit, double slit, triple and quadruple slits and a square slit. We then compared some of our data with theoretical approximations of the intensities and angles.

PRINCIPLES:

In this lab we studied Fraunhofer diffraction, which assumes that the light source (the laser) and the detector are an infinite distance from the aperture (the slit), so that the rays dealt with are all parallel. The diffraction arises from the phase differences of different waves being emitted from different parts of the aperture. These different wave amplitudes add constructively to form varying intensities at different locations along the screen. By integrating the wave amplitudes from the different parts of the aperture while accounting for phase shifting due to differences in distance, and then squaring the result, we find that the equation for intensity from a single slit is given by:

where slit width is equal to a and the angle Θ is the angle the location diverges from the axis. The general case for N slits and slit center-to-center separation d is given by:

where

Because the slit width d is necessarily smaller than slit separation a, the large rapid fluctuations in intensity come from the interference between adjacent slits. The overall shape of the intensity curve conforms to a shape determined by single slit diffraction. We can see typical interference fringes for multiple slit patterns in the diagram depicted

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below (this was taken from page 979 of Physics for Scientist and Engineers, by Jay Pasachoff and Richard Wolfson).

PROCEDURE:

We began the lab by setting up our equipment in the manner shown below. The laser we used was a He-Ne Class II laser with 0.95 mW/W maximum output and a wavelength of 632.8 nm

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The photodiode is mounted to the movable bar on the X-Y recorder, and powered by the voltage drop from the 9V power supply. The photodiode output is connected to the Y input of the recorder, so that as the bar moves perpendicular to the beam, the intensity of the diffraction pattern is recorded against the location. A piece of graph paper is placed against the plate and the pen is switched into the CHART position, which puts an electrostatic charge holding the paper to the plate. In order to make graphs of intensity vs. x position, the recorder is set have the bar sweep across the x axis at a constant speed, while a moveable draws a record of the intensity across the y axis.

In order to maintain a high accuracy in the recording of the intensity, we turn off all external light sources and draw the recordings. We first recorded the intensity patterns of single slit diffraction, using two different slits one after another. Then we made graphs of interference patterns that occur with double slits, using two slits of different widths and separations. Then we examined the interference patterns for three slits, four slits and five slits. We also looked at a square slits’ diffraction pattern.

CALCULATIONS:

See attached spreadsheets for template calculation of the theoretical intensity vs. angle graphs. These spreadsheets were made with the provided pre-made Excel template.

See lab book page 72 for other data and calculations.

RESULTS:

By comparing the graphs made with the X-Y recorder against those made with the Excel template, we can see that the observed shape of our curves closely matches those of the predicted curves. We can also see that the predicted intensity peak is within 10% of the actual intensity peak, for the single and the double slit experiments. In this lab we observed that narrowing the slits causes much greater intensity peaks.

For the square slit experiment, we found that while the thin slit caused diffraction along only one axis, the square slit allowed diffraction along two axis, so that the faintest points were along the lines y = x and the y = -x. This can be seen from diagrams on page 78 of the lab book.

In our analysis of the multiple slit experiment, we found that the number of slit means narrower and brighter fringes, with more dim fringes in between. This is because as more wave fronts are added coming from different slits, the equation for intensity becomes exponentially more complex, which results in a many more local minima and maxima.

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