Malus' Law of Polarization

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Overview:

Suppose that unpolarized light is incident on two linear polarizers. The angle between the polarizers is

and the intensity of the incident light is Io. The intensity of the light leaving the two polarizers is given by Malus' law:

The factor of 1/2 in the above equation comes about because the incident light is unpolarized. Malus' law demonstrates that there is a vector field, the E field, associated with light - an electromagnetic wave.

Goal of this Experiment:

Use the PASCO equipment to measure the dependence of transmitted intensity as a function of the angle between the two polarizers. A simple schematic of the setup to be used is shown below.

 

 The calibrated polarizers (shown below) should be mounted in placeholders.

Suggested Procedures:

  1. Set up the apparatus with no polarizers in place. Measure the intensity of light.
  2. Use a single polarizer and now measure the intensity of light. Is the light intensity reduced by a factor of 2? Is this result independent of the orientation of the polarizer?
  3. Replace the polarizer used in the previous step with the polarizer. Do you get the same results?
  4. Now make measurements with both polarizers in place. Make meaurements for various angles between the two polarizers.

Sample Data:

The plot below shows data taken with the setup of this experiment. The data displayed here were fit to a function of the form:

Questions:

  1. What is your estimate of the error in measuring the intensity of the light with no polarizers? With a single polarizer? With two polarizers? Explain how you arrive at your answers and measurements you make to back up your estimates.
  2. The polarizers are calibrated. How accurate are the degree scales on the polarizers? Can you think of any way to check this?
  3. What is your estimate of the error in the angle between the two polarizers?
  4. In the above analysis, what is the physical significance of the two constants, a and b?
  5. Can you think of ways to reduce the constant a?
  6. With respect to all the measurements you make in this experiment - would the use of apertures at the light source or before the fiber (or both) help? Describe any measurements you make to answer this question.
  7. With respect to all the measurements you make in this experiment - would it help to use lenses to focus the light? Describe any measurements you make to answer this question.