Two-Slit Interference

[ HomePage | Experiments | Equipment | Data Analysis | Software | Techniques ]

Overview:

Suppose light is incident on two slits of width a and spacing b. The intensity of the pattern created by interference and diffraction is given by:

Goal of this Experiment:

The goal of this experiment is to measure intensity as a function of position of the pattern produced by interference and diffraction effects as light passes through a pair of slits. A schematic of the set-up is shown below.

The PASCO system has a slide with four pairs of slits with various slit widths and spacings. The motorized linear translator is shown below:

 

Suggested Procedures:

 

  1. Determine the velocity of the motorized linear translator.
  2. Measure the intensity of the pattern as a function of position by starting the smaller fiber at one side of the pattern and allowing it to traverse the entire pattern while collecting data.
  3. Repeat the above using the larger fiber.
  4. Repeat the above using pairs of slits with different widths and/or spacings.

Sample Data:

A picture of a typical two-slit patter was taken with a digital camera:

From this picture can you say something about the ratio of the slit-width to slit-separation ?

We used a diode laser to illuminate a two-slit aperture (slit-width of 0.04 mm and separated by 0.25 mm). A fiber optic cable attached to a photodiode connected to a Mac via ULI interface read out the intensity. The fiber was mounted in a motorized linear translator which swept the fiber along the "screen" or along the y-axis at 0.17 mm/sec. The slit to fiber-optic distance was approximately 108 cm. The ULI measures intensity vs time - use the velocity to convert to intensity vs distance.

The red points are the data and the dashed curve is the product of interference and intensity:

N = arbitrary normalization
a = slit width
d = slit separation
y measures distance along the "screen"

The only parameter varied to overlay the curve on the data was the normalization, N. Note that the overall size of the pattern in the central maximum (diffractive) region (11 peaks) was a little over 1.5 cm.

Eric Scott provided the fiber-optic system and Matt Bavender set up the optics to clean up the laser beam for this exercise. Alex Dzierba and Matt took the data.

 

 

Questions:

 

  1. What is the error in your measurement of the velocity of the linear translator?
  2. What precision and data averaging settings should be used while collecting data?
  3. Does the size of the fiber make a difference in your intensity measurements? The data above were taken with a fiber of diameter 1 mm - does this account for the fact that the measured intensity does not fall to zero where expected ?
  4. Compare the data collected using pairs of slits with different spacings and widths--do they behave as expected?