Studio Session 6

Electromagnetic waves

In classical physics light is assumed to be an electromagnetic wave.  Electromagnetic waves are categorized according to their frequency f or, equivalently, according to their wavelength λ.  The speed of any electromagnetic waves in free space is the speed of light c = 3*10⁸ m/s.  Electromagnetic waves can have any wavelength λ or any frequency f as long as λf = c.  Visible light has a wavelength range from ~400 nm to ~750 nm.  Violet light has a wavelength of ~400 nm, and a frequency of ~7.5*10¹⁴ Hz.  Red light has a wavelength of ~700 nm, and a frequency of ~4.3*10¹⁴ Hz.

Electromagnetic (EM) waves are changing electric and magnetic fields, carrying energy through space.  EM waves require no medium, they can travel through empty space.  Let E denote the electric field vector and B the magnetic field vector of the EM wave.  For electromagnetic waves E and B are always perpendicular to each other, and perpendicular to the direction of propagation of the wave.

In general we pay more attention to the electric field E, because detectors such as the eye, photographic film, and CCDs interact with the electric field.

Electromagnetic waves are transverse waves.  In this session you will investigate various polarization effects.

Equipment Needed:

• Optical rail with post holders
• Pasco light sensor (CI-6504A)
• Diode laser
• 3 polarizers in rotation stages
• Glass slide
• Screen

Open a Microsoft Word document to keep a log of your experimental procedures, results and discussions.  This log will become your lab report.  Address the points highlighted in blue.  Answer all questions.

The inverse square law

All electromagnetic waves transport energy through space.  If a small source, for example the filament in a light bulb, emits light, the light can be seen from every direction.  At a distance r from the source, the light energy emitted by the source has spread over an area of 4πr², the surface area of a sphere with radius r, centered at the source.  Since this area increases with the square of the distance from the source, the energy flux or intensity I of the electromagnetic light wave, i.e. the energy per unit area per unit time, decreases proportional to the inverse square of the distance from the source.

I proportional 1/r²

This inverse square law is a consequence of energy conservation.
The energy of any wave is proportional to the square of its amplitude, so E²_max is proportional 1/r², or E_max is proportional 1/r.  The amplitude of an electromagnetic wave emitted by a point source (ideally a single accelerating charge) decreases as 1/r.

Experiment 1:

A small bright light bulb will be your point source of light, and you will use the Pasco light sensor (CI-6504A) to monitor the intensity as a function of the distance between the filament and the sensor.  The sensor connects to the Pasco 850 interface and outputs light intensity falling onto its active area measured in arbitrary units.  You will check if this intensity decreases proportional to the inverse square of the distance between the sensor and the source.

• The light bulb and the sensor are mounted on the optical rail.  The sensor and the filament of the light bulb should be at the same height and face each other.
• Plug the sensor into channel B of the Pasco 850 interface.
• Open the Capstone program.
• In the Capstone program, click the Hardware Setup button, double click Analog Channel B and choose to add a light sensor.
• From Displays, select the Digits icon and choose to measure Light Intensity (%).
• In the Controls panel select the Fast Monitor Mode and then click the Monitor icon.
• The light intensity will be displayed.  Initially it is proportional to the amount of background light falling onto the sensor.  To keep this background as low as possible, turn off the room lights.
• Record the background intensity I_B in units of %.

• Turn on the light bulb by rotating the lens counterclockwise and removing it completely.
• Let d_sb be the location of the sensor base on the optical rail.  The initial location should be 20 cm.
  
• The actual distance, d_act, between the filament tip and the sensor at d_sb = 20 cm is 5 cm.
• The offset distance d_off = d_sb - d_act is 15 cm.
• Download and open this Excel file.  It contains a table with the following headings.

• Move the sensor back in 2 cm steps and record the measured intensity I for each sensor base position d_sb in the table for 10 successive base positions.  When you are done taking data, close the Capstone program.
• Create calculated columns, r = d_sb - d_off, 1/r², and I = I - I_B.  I - I_B is the measured intensity I at a distance r = d_sb - d_off from the source.
• Produce a plot of I - I_B versus 1/r².  If the intensity decreases proportional to the inverse square of the distance between the sensor and the source, then this plot should show a straight line. 
• Label the axes of your plot.  (Intensity (I) versus 1/distance² (cm^-2))   Paste the plot into your log.
• Discuss your result with your group members and record the main points of your discussion.  Does your plot show a straight line?  If yes, what does this mean?  If no, what could be the reason for this result?

Polarization

Activity 1:

If light propagates through a transparent material such as water or glass, it interacts in various ways with the atoms or molecules that make up the material.  This interaction can be wavelength and polarization dependent.  Due to the interaction, light moves through a transparent material with an apparent speed v = c/n.  The index of refraction n is a property of the material.  It is greater than 1, so that v is less than c.  In most transparent materials the index of refraction depends slightly on the wavelength of the light, and in some materials it depends on the polarization.

Linear polarization:  An ideal linear polarizer is a material that passes only light waves for which the electric field vector is parallel to its transmission axis.  If E₀ is the incident field vector and the angle between E₀ and the transmission axis is θ, then the magnitude of transmitted field vector is E₀ cosθ, and its direction is the direction of the transmission axis.  The intensity I of an electromagnetic wave is proportional to the square of the magnitude of the electric field vector.  We therefore have

I_transmitted = I₀ cos²θ.

Polarizers with parallel transmission axes	Polarizers with perpendicular transmission axes	Polarizer 3 between polarizers 1 and 2.

Spend a few minutes exploring with the three pieces of linear polarizing material provided to you in an envelope.

Examples:

• Use one polarizing sheet as a polarizer and the other as an analyzer.  Observe the change in transmitted light intensity as either of the sheets is rotated.  Describe and comment on your observations.  This combination acts as a "light valve."
• Light reflected from smooth surfaces is polarized.  Look through a single polarizer at the light reflected from a shiny floor, smooth table top, or sheet of glass.  Describe and comment on your observations.
• Light from LCD screens is polarized.  Look through a polarizer at the screen of your laptop or cell phone.  Describe and comment on your observations.

Put the pieces of polarizing materials back into the envelope for the next lab session.

Experiment 2:

In this experiment you will use a linear polarizer to produces a polarized beam and then pass this beam through a second polarizer whose transmission axis makes an angle θ with respect to the transmission axis of the first one.  You will check that I_transmitted = I₀ cos²θ.  This is called the Law of Malus.

Important!

Do not move the bases on the rail.  Do not remove the components from the post holders.  Only adjust the height and orientation of the components.

• Plug the light sensor into channel A of the Pasco 850 interface.
• Open the Capstone program.
• In the Capstone program, click the Hardware Setup button, double click Analog Channel A and choose to add a light sensor.
• From Displays, select the Digits icon and choose to measure Light Intensity (%).
• In the Controls panel select the Fast Monitor Mode and then click the Monitor icon.
• The light intensity will be displayed.  Initially it is proportional to the amount of background light falling onto the sensor.  Make sure the sensor's "Gain" switch is set to 1.  To keep this background as low as possible, turn off the room lights.
• Record the background intensity I_B in units of %.
• The light sensor should be tightened to the optical rail at ~ 80 cm on the rail.
• Your light source for this experiment is a diode laser.  It should be tightened to the optical rail at ~40 cm.
• Two polarizers should be mounted between the laser and the light sensor at ~ 60 cm, with their transmission axes aligned vertically.  The polarizer holders should have their dial sides facing away from each other.  Make sure the polarizer disks are perpendicular to the laser beam.
• Adjust the height and angle of the laser, so that the laser beam falls onto the sensor window.  Monitor the light intensity.  (The detector is probably saturated.)
• Loosen the screw on top of the laser and rotate the laser so that the light intensity changes to ~75% - 85%.   Then tighten the screw again and also tighten the laser post in its post holder.  For the remainder of this experiment leave the laser and sensor undisturbed.
• After the laser light has passed through the polarizers, it is ~100% polarized along the vertical direction, since the transmission axis of each polarizer is vertical.

In Excel create a table.

• You will now rotate the second polarizer with respect to the first one.  Start by recording the measured intensity for zero degrees, when both polarizers are aligned.
• Rotate the second polarizer in 10^o steps.  For angles between 0 and 180^o in 10^o steps measure and record the intensity I in the table.
• When you are done taking data click Stop.
• Create calculated columns I - I_B and I₀*cos²(angle), with the angle in radians.  I₀ is the intensity you measured when the second polarizer angle was 0.
• Create a plot of I - I_B and I₀*cos²(angle) versus angle (rad).  Label the axes.
• Paste the plot into your log.
• Discuss your result with your group members and record the main points of your discussion.  Have you verified the Law of Malus?  How can you tell?  No experiment is perfect, there are always uncertainties.  Are your uncertainties small enough so that you can tell one way or the other.  Make reasonable arguments.

Polarization by reflection

When unpolarized light is incident on a boundary between two transparent materials, for example on an air-glass boundary, then the reflected and transmitted components are partially plane polarized.  The reflected wave is 100% linearly polarized when the incident angle is equal to the Brewster angle θ_B, where tanθ_B = n₂/n₁.  The Brewster angle for reflecting off glass is between 50^o and 60^o.

Experiment 3:

You will reflect the light from a diode laser off a glass plate.  You will make sure that the incident angle is close to the Brewster angle and verify that light polarized in the plane of incidence it will not be reflected at the Brewster angle.  The plane of incidence is a plane perpendicular to the reflecting surface that contains the incident beam.

If the reflecting surface is horizontal, then the plane of incidence is vertical.  The reflected light at the Brewster angle is horizontally polarized and can be blocked by a polarizer with a vertical transmission axis.  If the reflecting surface is vertical, then the plane of incidence is horizontal, and horizontally polarized light will not be reflected at the Brewster angle.  Then the reflected light is vertically polarized at the Brewster angle and can be blocked by a polarizer with a horizontal transmission axis.  You will reflect the laser light off a vertical glass surface (a microscope slide) and find the Brewster angle.

• Set up the components on the rail as shown on the right.  Turn the diode laser so that it shines on the middle of a glass slide in a holder on a rotation stage.  The surface of the slide is vertical.  The angle of incidence can be changed by rotating the stage.  Fix the rotation stage at 0.  Rotate the post in the holder until the light reflecting off the slide reflects back onto itself in the horizontal direction, and then tighten the post in the post holder.  (Block the transmitted beam to prevent it from shining into another person's face.)
• Rotate the polarizer in front of the screen by 90^o, so that its transmission axis is horizontal.  It now blocks vertically polarized light.
• Using the rotation stage, rotate the slide approximately 55^o.  Follow the reflected beam with the screen, by rotating the arm it is mounted on.  Find the angle at which the reflected intensity is lowest.
• Iterate by adjusting the transmission axis of the polarizer and the incident angle until the reflected intensity is practically zero.  Record the angle through which you have rotated the rotation stage.  This is the Brewster angle for the glass slide in air.
• Use this measured value to find the index of refraction of the microscope slide.
  We have tanθ_B = n_glass/n_air = n_glass, since n_air = 1.
• Is your value for n_glass reasonable?

• Keep the rotation stage fixed at the Brewster angle and rotate the polarizer.  You should see a reflected beam.  At the Brewster angle the reflected beam should be 100% vertically polarized.
• How do glare reducing sunglasses work?

Convert your log into a lab report.  See the grading scheme for all lab reports.

Name:
E-mail address:

Laboratory 6 Report

• In one or two sentences, state the goal of this lab.
• Make sure you completed the entire lab and answered all parts.  Make sure you show your work and inserted and properly labeled relevant tables and plots.
• Add a reflection at the end of your report in a short essay format.

Save your Word document (your name_lab6.docx), go to Canvas, Assignments, Lab 6, and submit your document.