Ph 122 quark%/~bland/docs/manuals/ph122/polar/polar.doc
December 28, 2005
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. Can you find it? Try reflection from the waxed floor in the hall. 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.)
C. Properties of the Polaroids.
(1) Arrange the apparatus as shown in the figure. Put the light source about 4 inches away from the polaroids.
2) Now measure the light intensity with the photometer with no filters in the light path; we will call this intensity IA. Note that there is sometimes a zero offset that has to be nulled out. (Check the zero offset by blocking the light with your hand and seeing if the needle goes to zero.) So, choose a scale for measurement (a), set the zero offset, and do not change scales while taking this and the following two measurements.
3) 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 in the two following cases:
(a) With one polaroid filter in the light path; we will call this intensity IB.
(b) With two polaroid filters in the light path, rotating one of them to get maximum transmitted light; we will call this intensity IC.
Make predictions for IB and IC, and write down the predicted intensities.
4) Now measure the intensities IB and IC. How do they compare with your predictions?
5) What additional process must be taking place in the Polaroid? [Hint: Why are IB and IC not equal? Is the assumption that the allowed polarization is transmitted without attenuation correct?] Can you make a more accurate theory of the operation of the Polaroid filters which lets you predict an expected value for IC?
D. Testing the Law of Malus.
1) 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 / Imeas / Itheor / cos2 q0 / 9.97 / 9.970 / 1
15 / 9.52 / 9.302 / .933
30 / 6.92 / 7.478 / .75
. / . / . / .
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, remember to convert degrees to radians; to do this in Excel talk, you could 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.)
4) Theory predicts that Itheor = Imax cos2 q . Calculate Itheor for each value of q, using as Imax the largest value of I which you measured. Make a plot with q on the x axis, showing both the measured and the theoretical values for I. Compare them. Discuss any systematic differences between the measured and the theoretical curves.
(5) 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. Determine the slope of the best straight-line fit to your data, and compare it with your actual value of Imax.
[To determine the slope, you can have Excel put a trend line on the curve. Be sure and specify the option which requires the intercept to be zero and the option which displays the equation on the graph. If you want to know the error on the fitted 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.]
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 - 3