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University of Virginia Physics Department
Name Date Partners
Lab 11 - Polarization
OBJECTIVES
- To study the general phenomena of electromagnetic wave polarization
- To investigate linearly polarized microwaves
- To investigate linearly polarized visible light
OVERVIEW OF POLARIZED ELECTROMAGNETIC WAVES
Electromagnetic waves are time varying electric and magnetic fields that are coupled to each other and that travel through empty space or through insulating materials. The spectrum of electromagnetic waves spans an immense range of frequencies, from near zero to more than 10^30 Hz. For periodic electromagnetic waves the frequency and the wavelength are related through c = λ f , (1) where λ is the wavelength of the wave, f is its frequency, and c is the velocity of light. A section of the electromagnetic spectrum is shown in Fig. 1.
In Investigation 1, we will use waves having a frequency of 1.05 × 10^10 Hz (10.5 GHz), corresponding to a wavelength of 2.85 cm. This relegates them to the so-called microwave part of the spectrum. In Investigation 2, we will be using visible light, which has wavelengths of 400 – 700 nm (1 nm = 10-9^ m), corresponding to
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1 MHz
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VISIBLE LIGHT
Frequency, Hz Wavelength, m
Gamma rays
X rays
Ultraviolet light
Infrared light
Short radio waves Television and FM radio AM radio
Long radio waves
1 nm
1 mm 1 cm
1 m
1 km
1 Å
Microwaves 1 GHz
1 THz
1 μm
10
Fig. 1. Section of the electromagnetic spectrum.
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frequencies on the order of 4.3 × 10^14 -7.5 × 10^14 Hz. These wavelengths (and hence, frequencies) differ by nearly five orders of magnitude, and yet we shall find that both waves exhibit the effects of polarization. Electromagnetic waves are transverse. In other words, the directions of their electric and magnetic fields are perpendicular to the direction in which the wave travels. In addition, the electric and magnetic fields are perpendicular to each other. Fig. 2 shows a periodic electromagnetic wave traveling in the z -direction. Study this figure carefully. We will refer to it often.
When the electric field of a wave is oriented in a particular direction, that is to say, not in random directions, we say the wave is polarized. In this workshop, we will investigate the polarization of two types of electromagnetic waves that have somewhat different wavelengths and frequencies: microwaves and visible light. We will both produce and analyze polarized waves.
Electromagnetic waves are produced whenever electric charges are accelerated. This makes it possible to produce electromagnetic waves by letting an alternating current flow through a wire, an antenna. The frequency of the waves created in this way equals the frequency of the alternating current. The light emitted by an incandescent light bulb is caused by thermal motion that accelerates the electrons in the hot filament sufficiently to produce visible light. Such thermal electromagnetic wave sources emit a continuum of wavelengths. The sources that we will use today (a microwave generator and a laser), however, are designed to emit a single wavelength.
The inverse effect also happens: if an electromagnetic wave strikes a conductor, its oscillating electric field induces an oscillating electric current of the same frequency in the conductor. This is how the receiving antennas
Direction of Propagation
Fig. 2. Periodic electromagnetic wave, E = vector of the electric field, B = vector of the magnetic field.
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If both x - and y -components are present and their phase difference is zero (or 180°), the wave will be linearly polarized in a direction somewhere between the x -direction and the y -direction, depending on the relative magnitudes of E x and E y (see Fig. 4a). Mathematically such a wave is described by:
= + =( E ± E )sin⎛^2 ( z − ct ) x y x y
E E E i j , (4)
where the plus sign refers to a phase difference of zero and the minus sign
to one of 180° ( π radians). The angle θ between this polarization direction
and the x -direction is given by
x
y E
E
tanθ =. (5)
If the phase shift is not zero (or 180°), the wave will not be linearly polarized. While we will only investigating linear polarization in this lab, it is useful to know something about other types of polarization. Consider the case where the magnitudes are equal, but the phase shift is ±90° (± π / radians). In other words:
Ex = E y and 2
The resulting wave, called a circularly polarized wave, can be written:
± ⎛^ −
= + = E sin⎛ 2 ( z − ct ) cos^2 ( z ct ) x y
E E E i j (7)
by making use of the fact thatsin ( α + π/ 2 )=±cos α. With the plus sign,
this equation describes a wave whose electric field vector, E , rotates clockwise in the x -y plane if the wave is coming toward the observer. Such a wave, illustrated by Fig. 4b, is called a right circularly polarized wave. With the minus sign, the equation describes a left circularly polarized wave.
θ Ex
E (^) y
y
x
E
a) (^) b) c)
E E x
y (^) y
x
Fig. 4. a) Linear, b) circular, c) elliptical polarization.
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With the phase shift still ±90°, but with different magnitudes
E (^) x Ey
≠ and φ =± , (8)
the E vector will still rotate clockwise or counterclockwise but will trace out an ellipse as shown Fig. 4c. If there are many component waves of
different E x , E y, and φ, the resulting wave will be unpolarized.
Polarized electromagnetic waves can be obtained in two ways:
- by using sources, such as certain lasers, that produce only waves with one plane of polarization, or
- by polarizing unpolarized waves by passing them through a polarizer , a device that will let only waves of one particular plane of polarization pass through.
Some sources of electromagnetic waves generate linearly polarized waves. Examples include the microwave generator we'll use today as well as some types of lasers. Other sources generate unpolarized waves. Examples include thermal sources such as the sun and incandescent lamps. One way of producing linearly polarized electromagnetic waves from unpolarized sources is to make use of a process that directs waves of a given polarization in a different direction than waves polarized in a perpendicular direction. Earlier we noted that the electric field of an electromagnetic wave incident upon a wire induces an oscillating current in the wire. Some energy will be lost through ohmic heating, but more will be re-radiated (scattered). Only the component of the oscillating electric field that is parallel to the wire will induce a current and be scattered. The electric field component perpendicular to the wires, on the other hand, will be essentially unaffected by the wires (assuming a negligible wire diameter). Hence, both the scattered and unscattered electromagnetic waves are linearly polarized. For microwaves, we can (and will) use an array of actual wires. For visible light, we use a Polaroid filter. Polaroid filters are made by absorbing iodine (a conductive material) into stretched sheets of polyvinyl alcohol (a plastic material), creating, in effect, an oriented assembly of microscopic "wires". In a Polaroid filter the component polarized parallel to the direction of stretching is absorbed over 100 times more strongly than the perpendicular component. The light emerging from such a filter is better than 99% linearly polarized.
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P, and θ' is the angle between P and the second polarizer, P'. But P' is at right angles to the initial wave's polarization and so θ + θ' = 90°. Hence,
cos 2 θ' = sin^2 θ. Using another trigonometric identity
(sin 2 θ = 2 sin θ cos θ ), we finally get I' = 0.25 I i sin^2 2 θ. We can see we
get the maximum transmission when θ = 45° (sin 2×45° = 1) and that it is
one quarter of the intensity of the incident polarized waves ( I i).
INVESTIGATION 1: MICROWAVE POLARIZATION
For this experiment, you will need the following:
- PASCO Gunn diode microwave transmitter
- PASCO microwave receiver
- Wire grid polarizer
Activity 1-1: Polarization of a Gunn Diode
- Inside the microwave generator is a solid state device called a Gunn diode. When a dc voltage is applied to a Gunn diode, current flows through it in bursts at regular intervals. For your diode, these bursts come at 9.52 × 10-11^ seconds apart causing, in addition to the dc current, an ac current at 1.05 × 10^10 Hz (10.5 GHz). As a result, a large ac voltage, oscillating at that frequency, is present across the slot, and so a wave is radiated from the horn. The electric field of this wave oscillates in the same orientation as the Gunn diode. The polarization of an electromagnetic wave is determined by the direction of the electric vector E. The magnetic field B encircles the current in the Gunn diode and so emanates in the orientation perpendicular to E. Important Note: The Gunn diode is place inside the generator in a way that the electric field will oscillate vertically when the knob on the back is placed at 0º.
- Just inside the horn of the receiver is a microwave detector. In addition, there is some circuitry, which amplifies the signals received by the detector and outputs this amplified signal to a d’Arsonval meter and to an external output. The amplification, or alternatively its inverse, the sensitivity, (also labeled METER MULTIPLIER), is controlled via two knobs. The VARIABLE SENSITIVITY knob allows for fine adjustment. As you turn up the sensitivity (from 30 to 1), the signal is amplified more and more. To peg the meter means to allow the needle to go beyond the maximum value on the scale. It is imperative that you NOT peg the meter as doing so can damage it! If you find the meter pegged, immediately turn down the sensitivity and/or move the receiver away from the microwave generator!
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CAUTION: DO NOT ALLOW THE RECEIVER’S METER TO PEG AT ANY TIME!
- Set up the generator and receiver as shown in Fig. 6.
Prediction 1-1: With what relative orientation of the transmitter and receiver do you expect to find minimum intensity? What does this tell you about the electromagnetic microwaves?
- Set the knobs on back of both pieces so the angle indicator is at 0°. Adjust the sensitivity on the receiver to obtain a signal near 0.5 on the meter. If you cannot achieve this with a sensitivity of 10 or 3, move the receiver closer to the generator. Rotate the receiver and verify that it is sensitive to the polarization of the wave. Return the receiver angle to 0º.
Fig. 6. Use this arrangement to test for polarization.
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Question 1-2: With what orientation of the polarizer did the receiver indicate the highest intensity? The lowest?
- Now set the generator’s angle to 90º, turn up the sensitivity to 1, and repeat the experiment.
Question 1-3: At what angle (relative to the generator) for the wire grid polarizer does the meter read a maximum?
INVESTIGATION 2: POLARIZATION OF A HIGH-INTENSITY LAMP
In this investigation, the unpolarized light from a high-intensity lamp will be linearly polarized. This polarization will be investigated with a second Polaroid analyzer. In addition, a third polarizer will be added to investigate the effect of the orientation of a third polarizer on the intensity.
For this you will need the following:
- Optical bench with lens holders
Summary: We learned in our study of microwave polarization that the metal grid wires do not allow electric fields to pass when the field is parallel to the direction of the wires. However, when the wires are oriented perpendicular to the electric field direction, the electric field is able to pass through. We also found that we could use a wire grid polarizer to rotate the electric field vector.
Note: In the remainder of the workshop we will investigate the polarization of visible light. For the next three Investigations, it will be necessary at times to turn off all of the lights in the lab to obtain the best results.
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- Polarizer
- Bausch and Lomb polarized light demonstrator kit
- Small support stand
- Desk lamp (high intensity light source)
- PASCO light sensor and cable
Activity 2-1: Linearly Polarized Light and Malus' law
Note: The light sensor that will be used for the rest of the experiments is a PASCO light sensor. It is a photodiode with a sensitivity that ranges from 320 nm to 1100 nm. Make sure not to allow the output voltage from the sensor to go above 4.75 volts. At this point, the sensor is saturated and you will not get accurate readings.
- Set up the lamp, polarizers, and light sensor as shown in Fig. 7. DO NOT TURN YOUR LAMP ON YET. Make sure your lamp is on the opposite end of the table from the computer and is pointing towards the wall, not towards the center of the room. We want to minimize the interference of the light coming from the desk lamp into each other's light sensor.
- The heat-absorbing filter (item #1 in the box of components) should be mounted on the small support stand in between the light source and the first polarizer.
- Ensure that the heights of the light, heat absorbing filter, polarizers and light sensor are lined up. Your lamp can now be turned on.
Fig. 7. Setup of the linearly polarized light experiment.
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- When you feel that the reading has stabilized, press Keep. A box will pop up that asks you the angle of the polarizer. Type in “-90” and press Enter.
- Adjust the analyzer to an angle of -80º. The voltage output will now be shown as before. Press Keep and type in the angle.
- Adjust the angle of the analyzer in 10º steps from -90º to 90º. Repeat step 11 until all of the values are entered, putting in the respective values for the angles. This can go rather quickly with one person changing the angle and another person operating the computer. Once Keep has been selected, the next angle can be changed by one group member while another is entering the angle into the computer.
- When you are finished entering data, click on the red square next to Keep to stop data collection.
- Print out your graph table for your report. Only print one per group. You may need to print it twice to include all the data.
- At the bottom of the screen, there should two graphs minimized. Bring up the graph titled I vs. Angle so you can see the graph of your light intensity plotted versus angle. If you see a fit to your data, you have brought up the wrong graph.
Question 2-1: What does your graph look like? Does it follow the curve you would expect?
- Minimize this graph, and maximize the second graph titled Fit Malus L11A2-1. You will see your data plotted along with a fit. You could have easily entered this fit into Data Studio yourself, but we have done
it for you to save time. We have fit intensity I versus angle θ using a
function of the form I 2 = I 1 cos^2 θ+ IB.
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Question 2-2: What values did you find for the intensities I 1 and I (^) B? Enter your values below. What does the value for I (^) B represent? Explain the results of your equation. What is physically happening? I (^) 1 IB
Question 2-3: Is it possible that I B is not constant? Explain. How could you minimize I B?
Question 2-4: Does it appear that Malus' Law (Eq. 9) is obeyed? If not, please explain.
- Print out your graph and attach it at the end of your lab. Only print one per group.
Note: The following experiment will use all of the setup from Activity 2-. Leave everything in place.
Activity 2-2: Three Polarizer Experiment
- Using the setup from Activity 2-1 , set the two existing polarizers so that they are crossed (e.g. the polarizer at 90º and the analyzer at 0º).
Make sure to leave the heat absorbing filter in place between the lamp and the polarizers!
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Question 2-5: Explain your findings in terms of the orientation of the electric field after the light travels through each polarizer. Why would the angle found in step 4 produce the maximum intensity?
INVESTIGATION 3: BREWSTER’S LAW
An alternative way to produce linearly polarized light is based on Brewster’s law. A wave falling on the interface between two transparent media is, in general, partly transmitted and partly reflected. However, there is a special case in which the directions of the transmitted and reflected waves are perpendicular to each other, as shown in Figure 9.
α (^) α
β
n 1
n 2
Incident Ray Reflected Ray
Refracted Ray
Fig. 9. Reflection at Brewster's angle. The electric field of the p wave (represented by short lines, │ ) is in the plane of the paper while the electric field of the s wave (represented by dots, ● ) is perpendicular to the page.
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The component of the wave whose electric vector E is in the plane of the page , called the p wave , is not reflected at all but completely transmitted when the incident angle is α (called Brewster’s angle) from the normal. The electric field of the p wave is represented by the short lines (│) in the figure. Meanwhile, the reflected light contains the remainder of the wave, the component whose electric vector oscillates perpendicular to the plane of the page. Therefore, the light that is reflected is totally polarized. This second wave is usually called the s wave. The electric field of the s wave is represented by the dots (●) in the figure.
The angle of incidence satisfying the condition of Brewster’s law, called Brewster’s angle , is easily obtained from Fig. 9. Noting that
and using Snell’s law ( n 1 sin α= n 2 sin β,where n 1 is the index of
refraction of the medium containing the incident ray, and n 2 is the index of refraction of the medium containing the refracted ray), we can show:
tan cos
sin
sin
sin sin
sin 2
n
n
. (11)
In the case that you will be looking at in class, the index of refraction of the first medium, n 1 is equal to the index of refraction of air. For this workshop, this will be taken to be unity. Putting this into Eq. (11), we get: n = tan α (12) where n is the index of refraction of the glass plate.
Brewster’s law is just a special case of the Fresnel equations that give the amplitudes of the transmitted and reflected waves for all angles for the two polarizations.
The polarization upon reflection is rarely used to produce polarized light since only a few percent of the incident light are reflected by transparent surfaces and become polarized (metal surfaces do not polarize light on reflection). But the fact that light reflected by glass, water, or plastic surfaces is largely polarized enables one to cut down glare with Polaroid glasses or Polaroid photographic filters.
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- Small support stand
- Polarizer
- Spectrometer stand
WARNING: LASER LIGHT CAN DAMAGE THE EYES. NEVER
LOOK DIRECTLY INTO THE BEAM OR AT LASER LIGHT
REFLECTED FROM METAL, GLASS OR POLISHED
SURFACES.
Activity 3-1: Determination of Brewster’s Angle
Prediction 3-1: You will be using crown glass as your Brewster window in the following experiment. What angle do you expect to find, knowing the index of refraction of crown glass (see Appendix A)?
- Mount the 2.5” glass plate in the slot atop the small turntable. Use the nylon screws to hold the plate in place perpendicular to the stand. This will serve as your Brewster window. Place the turntable on the table next to the middle of the optical bench. Do not move the optical bench! It is very fragile. See Fig. 12.
Fig. 12. Diagram looking from above the apparatus. The light from the laser travels through the polarizer and to the glass plate, where some of it is reflected and some is refracted.
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- Make sure that the laser emits a single pencil of light (i.e., no “beam spreader”). Adjust the laser so that the beam produced is horizontal and is incident upon the glass plate. The distance between the laser and glass plate should be about 50 cm, but this does not require a measurement.
- Place a polarizer and holder on the table in between the laser and the glass plate, so the light travels through the polarizer.
Question 3-3: According to the discussion of Brewster's angle, only the s wave is reflected at Brewster's angle (see Fig. 9). If the s wave is not present in the incident light, then the Brewster’s angle can be found quite easily; it will be the point at which no light is reflected. We want to utilize the polarizer to only allow the p wave to be incident upon the glass plate. Then, when the plate is at Brewster's angle, all the light will be transmitted through the glass and none will be reflected. At what angle should we set the polarizer to transmit only the p wave? Polarizer angle for only p wave transmission: Explain how you decided upon this angle:
Note: Make sure that the polarizer does not completely block the laser light. To check this, look at the glass plate to ensure that there is light incident upon it. Also try to find the refracted beam. No matter what the angle of the glass plate is with respect to the beam, there will always be a refracted (transmitted) beam – the p wave is always refracted.
- Set the polarizer at the angle you just determined in Question 3-3.
- You may find that your laser is polarized (some of our lasers are, some aren’t). If so, you may have to rotate the laser about its axis so that enough of the beam passes through the polarizer to clearly visible.
- Let the reflected light fall upon a notebook size piece of white paper as a screen to show the reflected ray, rotate the turntable until you find the position at which the intensity of the light reflected by the plate becomes a minimum. You may find that by alternately "tweaking" the polarizer angle and the plate angle, you can make the reflected ray completely vanish.
