Polarization Experiment 4

Name______Lab Partners______Instructor Name______

INTRODUCTION

Diffraction and interference experiments provide evidence that light may behave as a wave in some cases. They do not, however, indicate whether the waves are longitudinal or transverse. Polarization experiments demonstrate that light waves are transverse waves. In this experiment, you will produce and analyze linearly polarized light. You will also learn how linearly polarized light behaves when it reflects from certain materials.

THEORY

In one model, light is treated as transverse electromagnetic vibrations; that is, electric and magnetic fields oscillate in planes transverse (perpendicular) to the direction of propagation. Light is said to be unpolarized if the electric field vector is uniformly distributed in all directions in the plane perpendicular to the direction of propagation. Sometimes the unpolarized light is referred to as "natural" or "randomly polarized" light. If the electric field is along a single direction, the wave is said to be linearly (or plane) polarized. Figure 4.1 shows unpolarized light and linearly polarized light. Here, the direction of propagation of the wave is out of the page toward you.

Electric field from Electric field from unpolarized light polarized light Figure 4.1 To detect polarized light, one must use an analyzer, a device that transmits the electric field component parallel to one specific direction, known as the axis of transmission. The analyzer can also be used to polarize light. The function of the device determines whether we call it a polarizer or analyzer. When unpolarized light transmits through a polarizer, it will emerge as linearly polarized light with its electric field parallel to the axis of transmission of the polarizer. If linearly polarized light transmits through a polarizer, only the electric field component parallel to the axis of transmission is transmitted, see Figure 4.2. Mathematically, the component of the electric field

that is transmitted may be written as E = Eo cos , where Eo is the electric field strength in the incident wave, E is the transmitted electric field strength, and  is the angle between the incident electric field and the polarizer's axis of transmission. Since the intensity of the transmitted wave is proportional to the electric field squared, we may write the intensity of the transmitted light as 2 2 I = Io cos where Io = Eo . This equation is sometimes referred to as the Law of Malus.

Figure 4.2

If instead, we have a beam of unpolarized light incident on a polarizer, there will be as much light in the beam with its electric field parallel to the transmission axis as there is perpendicular to it. Therefore, the intensity of the transmitted light is (1/2) Io.

Figure 4.3

One of the most well-known applications of polarizing effects occurs with the use of polarizing sunglasses to reduce glare. Glare is essentially caused by the reflection of light from shiny surfaces. The glare is reduced because the polarizing material in the sunglasses blocks some of the reflected light whose state of polarization is perpendicular to the axis of transmission in the sunglasses for certain angles of reflection. The angle of incidence where light with a certain state of polarization is not reflected is called Brewster’s angle B, (also called the polarizing angle) and is given by tan B = n, where n is the index of refraction of the reflecting material, and the reflection occurs in air. You will observe this effect at the end of the experiment.

EXPERIMENT NO. 4

1. Check the state of polarization of the room lights by looking at the room lights through one of the polarizers and rotating it through 360o. Do you observe any significant variation in the intensity of the light transmitted through the polarizer?

Are the room lights polarized or unpolarized?

2. Place the flat sides of the polarizers together and observe the room lights through both polarizers at the same time. Rotate one of the polarizers until the intensity is minimum. Is any light transmitted through both polarizers when the intensity is minimum? If some light is transmitted, does it have any color?

If so, what is the color, and what do you conclude about how the polarizers behave as a function of wavelength (color)?

3. Figure 4.4 shows the setup you will use for most of the remainder of the experiment. The laser serves as the light source, polarizer A is manually rotated, polarizer B is rotated by a motor, and the detector senses the light intensity. You will not use both polarizers at the same time for some of the experiment.

Figure 4.4

Turn on the laser and position polarizer A between the laser and the detector. Polarizer B is not used for this part of the experiment. Open Exp 4 from the Start menu 1102 folder. Start recording the light intensity with the detector. Slowly rotate polarizer A and observe any variation in the intensity of the detected light. When the intensity is a minimum, record the polarizer angle reading on the index marker of the component holder.

Polarizer angle = ______

Is the laser light polarized?

The axis of transmission of the polarizer is along the 0 – 180-degree line on the polarizer. Use this information to calculate the angle the electric field of the laser light makes with respect to the vertical.

Angle electric field of laser light makes with the vertical = ______

4. Remove previous data set by clicking on Experiment and then on Delete all data runs. Replace polarizer A with polarizer B and collect a data set of the intensity versus the angle of the rotating polarizer B. Label and print a copy of a graph for each person. The rate of rotation of polarizer B is about 1 revolution every 45 seconds. In one revolution of the polarizer, how many intensity maxima are there? How many intensity minima are there?

Number of intensity maxima = ______Number of intensity minima = ______

Explain the reasons for the number of intensity maxima and intensity minima. Show figures with the orientation of the electric field and the axis of transmission of the polarizer.

5. Keep the data from step 4 on the computer screen. Move polarizer A about 10 cm from the detector and adjust it so that the transmitted light is minimum. Insert polarizer B about halfway between the laser and polarizer A. Collect a data set for the transmitted intensity when polarizer B is allowed to rotate through a couple of revolutions. Label and print a copy of the graph for each person. This graph must contain data from step 4 and step 5. Compare this set to the previous data set. Record the number of maxima and the number of minima when polarizer B rotates through 360 degrees.

Number of intensity maxima = ______Number of intensity minima = ______

Explain why there are an increased number of maxima and minima under these conditions. Use figures showing the orientation of the electric fields and the axes of transmission of the two polarizers.

6. Brewster’s angle occurs when the electric field of the light beam lies in the plane of incidence of the beam. The plane of incidence is the plane formed by the incident beam and the reflected beam. Place the acrylic semicircle and the angular scale on the optical bench, and allow the laser light to reflect from it. Insert polarizer A in between the laser and acrylic semicircle aligning it so that axis of transmission is horizontal. Rotate the semicircle to determine the angle of incidence at which the intensity of the reflected light becomes zero. This is Brewster’s angle. Record the angle. Note that reflected light will not completely disappear, instead, it will get blurry.

Brewster’s angle = ______

7. Use the equation tan B = n to calculate n for the acrylic semicircle.

n = ______

Use the standard value for n given by your TA to calculate the percent error in your measurement.

Percent error in n = ______

What do you think would happen if the electric field in the laser beam were perpendicular to the plane of the table?

QUESTIONS

1. A polarized beam of intensity I0 is directed into a device consisting of two polarizers. The beam is vertically polarized and the transmission axis of the second polarizer is 230 with respect to the vertical direction. If only 1/10 of the beam’s intensity is transmitted by the second polarizer, what is the orientation of the transmission axis of polarizer 1 with respect to the vertical direction?

2. Consider the situation you studied in Part 5 where the middle polarizer is rotated. Suppose the middle polarizer is rotated at 100 revolutions per minute. How many times per minute will you observe the light change from bright (maximum intensity) to dark (minimum intensity)? This effect, although not normally done with mechanical rotation, is the basis for making optical modulators that are used in high-speed digital communication systems.