Polarization

In this experiment we look at the properties of polarized light.

I. Theory

Electromagnetic waves (like light) consist of electric and magnetic fields, both oriented in directions perpendicular to the direction of propagation of the light. There are thus two independent directions for the electromagnetic field vector E. A Polaroid is made of a type of plastic, which transmits light with E parallel to a certain direction on the Polaroid, referred to as the axis of the Polaroid. Light with its E vector parallel to the axis passes easily through the Polaroid. However, light with the E vector perpendicular to the axis is totally absorbed by the Polaroid. This property can be used to measure the polarization of light, or to create a source of polarized light.

The Law of Malus gives the intensity transmitted through two Polaroids as a function of the angle q between their axes. The law is:

(1) The Law of Malus

When light reflects from a surface at a particular angle, called Brewster’s angle, the reflected ray is 100% polarized, with the direction of the E field in the plane of the reflecting surface. Brewster's angle is given, in terms of the indices of refraction, by

(2) Brewster’s Angle

II. Experimental Procedure

The light sources we shall use today project unpolarized light (that is, a mixture of light waves with all polarizations). However, the molecular structure of the Polaroids will polarize the light for us.

A. Orientation of the Polaroids.

Hold a pair of Polaroid filters together and look at the room lights through them. Observe the intensity of the transmitted light as you rotate the filters and describe what you see. Determine what marks on the filters will allow you to measure their orientations.

B. Measurement of Brewster's angle.

Look at light reflected from various things using a Polaroid. There is a certain angle of reflection for which reflected light is almost 100% polarized. Go into the hallway and find the reflection of the overhead lights off the waxed floor that is polarized. Use geometry to estimate qB and use eqn. (2) to calculate n for the wax used on the floor. (Here n1 represents air, so you can take n1 = 1.)

Q1. Is your result for the index of refraction for the wax on the floor reasonable? Explain how you know.

C. Properties of the Polaroids.

Arrange the apparatus as shown in the figure. Put the light source about 10 cm away from the Polaroids. With no filters in the light path, choose an appropriate scale.

Note that there is sometimes an offset that has to be zeroed out. Check the offset by blocking the light with your hand and seeing if the needle goes to zero. If it does not, adjust the zero offset so that the meter reads zero when you block the light with your hand. You should not change scales while taking the next three measurements. Measure the light intensity with the photometer with no filters in the light path; call this intensity IA.

Make a table in your lab book like the one below. You are going to carry out a sequence like this: Measurement; Prediction; Measurement; Revised Prediction; Measurement. You have just taken the first measurement. Enter it in the table, as a measurement of IA.

Meas. 1 / Pred. 1 / Meas. 2 / Pred. 2 / Meas. 3
IA
(no filter)
IB
(one filter)
IC
(two filters, rotated
for maximum
intensity)

According to the simple theory of the operation of a polaroid filter, it should completely absorb light of one polarization, while leaving light of the other polarization unaffected. Based on your value for IA, and this simple theory of Polaroid filters, predict what intensity should be measured with one polaroid filter in the light path; call this intensity IB, and enter your prediction on the table.

Now measure the intensity IB, and enter your result in the table. We anticipate that the agreement will not be perfect.

Your next job is to interpret the measurement that you just made. Think about what additional process must be taking place in the Polaroid. Hint: Is the assumption that the allowed polarization is transmitted without attenuation (lessening) correct? Revise your concept of the operation of the Polariod so as to explain the additional loss of intensity that you see. You may consult the instructor to see if your explanation makes sense.

Q2. What is your revised explanation of the operation of the Polaroids?

Use this new theory of attenuation of light by Polaroids to make a revised prediction for IB , and write this prediction in the table. (It should of course agree with the value you already measured for IB. )

Now, as a test of your new theory of the Polaroid, predict the intensity with two polaroid filters in the light path, rotating one of them to get maximum transmitted light; call this intensity IC. Enter this value into the table.

And here is your final test of theory with experiment. Measure the intensity IC, and enter the value into the table.

Q3. Did your revised theory work? Do you have any ideas for further perfecting it?

D. Testing the Law of Malus.

Now set up to measure the intensity Iq of the beam as a function of the angle q between the Polaroid planes. Start by setting the inner Polaroid at zero degrees. Then set the angle of the second Polaroid for maximum intensity, and adjust the photometer so that it reads 10.0 (full scale) with the light present, zero with the beam blocked. Using these settings, and without changing scales, take a complete set of measurements. Make a measurement every 15 degrees over the full range of 360 degrees.

angle q / cos2 q / Itheor / Imeas
0 / 1 / 9.970 / 9.97
15 / .933 / 9.302 / 9.52
30 / .75 / 7.478 / 6.92
. / . / . / .

Table 1. Typical data-table format.

Record your data directly on the computer, in an Excel spreadsheet, in a table as shown. In the column for cos2 q, you must convert degrees to radians; to do this in Excel talk, enter =cos(a2*pi()/180)^2 . (Here a2 is the address of the value of the angle q, and may be different on your spreadsheet.)

Theory predicts that Itheor = Imax cos2 q. Calculate Itheor for each value of q in excel, using as Imax the largest value of I that you measured. Make a plot with q on the x-axis, showing both the measured and the theoretical values for I.

Q4. Compare the theoretical and the measured curves. Discuss any systematic differences between them.

Make a second plot showing I (the measured value) versus cos2 q. From the relation Itheor = Imax cos2 q we expect that these points should lie on a straight line, with slope equal to Imax.

To determine the slope experimentally along with the error on the slope, use the Excel function: =linest(yvals,xvals,1,1) followed by (Ctrl)(Shift)(Enter), as described in the first write-up in this manual.

Q5. Compare your slope with your actual value of Imax. What could account for the discrepancy?

III. Equipment

Optical bench

Tensor lamp

Optical object box

2 Polaroid filters

Mount to hold two filters and one end of optical fiber

Pasco photometer (model 8020)

polarization - 1