Polarization by repeated reflection

Alexandra Sawaetwong
[Edited version]
Feb. 25th, 2002

Introduction

When unpolarized light strikes the surface of a transparent medium such as glass (used in this experiment) the refracted ray is partially polarized. When the reflected ray is at and angle of 90° to the refracted ray, the reflected ray is totally polarized. In this situation the refracted ray is at its maximum partial polarization. ip is the polarizing angle (the unpolarized light's angle from the transparent medium's norm), and n is the refractive index of the transparent medium.

The result is Brewster's law:

For glass n = 1.5 and ip = 56.31°.

At 34 degrees between the glass and the incoming ray the reflected light is completely oplarized since ...

To increase the percentage polarization light was passed through increasing numbers of glass plates at 34°.
 
Research question

What is the relationship between the percentage polarization of the transmitted ray and the number of glass sheets that it is refracted through in the series? In particular, how many pieces of glass does it take to polarize unpolarized light by 90%?

Hypothesis

The percentage polarization of the refracted ray through the series of glass sheets is expected to approach 100% exponentially, since the percentage polarization of the light is equal for each single piece of glass it is refracted through. If the percentage polarization through each glass is ~50% it would take a minimum of 5 sheets to polarize the light to approximately 90%.

Procedures

A Vernier light detector was taped to a clamp stand and connected to a computer. Three pieces of dark plastic were taped in front of the light detector to reduce the light intensity. All lights except a film strip projector were switched off. A convex lens was placed in front of the projector to collimate the unpolarized light. The first glass square was placed inside the diskette holder at a 34° angle to the table (figure 1).

The accuracy of the set up is checked by rotating a Polaroid over the glass above the reflected ray (figure 3). Ideally there would be no light coming through the Polaroid in one direction. When the Polaroid is in the first direction, reflected light shines through (as seen in the picture). When the Polaroid is in the second direction (rotated around 90 degrees) almost no reflected light shines through.

The zero for light intensity was set by placing two crossed Polaroids in front of the light detector. The side of a Polaroid was marked with tape, so the direction could be determined when rotating it around 90 degrees.

Fig 4 Note the green tinge due to absorption by iron impurities in the glass

.The Polaroid was held in front of the light detector (with the tape at the top). The intensity of the transmitted component was measured. The Polaroid was then rotated 90 degrees and the intensity was measured again.

A second glass was then added with cardboard padding of equal thickness so the angle was kept constant. Measurements were taken again and repeated with the third, fourth, fifth, etc. glass squares in place.

Data
 
Number of glasses vs. intensity for the Polaroid in one direction (with tape at the top) and in the other direction are shown in the Tables.

With this graph and equation, the number of glasses needed to polarize unpolarized light to approximately 98% can be calculated.
 
The Data Set below is plotted in Graph 1.
 

The percentage polarization (Graph 2) is the horizontal intensity over the corresponding total intensity. The total intensity is the intensity in the horizontal direction plus the intensity in the vertical direction.

Discussion

Ideally the intensity of light in the vertical direction should remain constant throughout, since the glasses are only reflecting light in the horizontal direction. The decrease in the intensity in the vertical polarization is caused by absorption of light in the plates.
 
Although the data has large errors, it supports the hypothesis. The results show that the relationship between percentage polarization, and number of glasses is exponential as expected. The results also prove that 7 glasses are needed to polarize unpolarized light up to 90% by repeated reflection.

Sources of error
and suggestions for further work:

Light absorption in the glasses is an undesired variable that causes the light intensity in the vertical direction to decrease and the reflected ray was not completely polarized meaning the angle of the glass squares was not exactly the polarizing angle.

Using thinner glass (like microscope cover slips) could reduce light absorption in the glass and a frosted glass can be placed in front of the light source to make it more uniform.

Using a coherent light source (i.e. a laser pointer) for this experiment may sound like a good idea, but it is not for two main reasons. The beam is too narrow, making it difficult to line the light detector to pick it up. If the narrow beam is scattered into a wider one, the intensity will become too weak. In addition, laser light is already partially polarized to begin with.