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.  Transverse waves can be polarized.  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 live journal of your experimental procedures and your results.  Include all deliverables, (data, graphs, analysis, outcome).  Write a 'mini-reflection' immediately after finishing each investigation, experiment or activity, while the logic is fresh in your mind.

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.  Imagine a point source emitting energy into 3D space.  How does the area of a spherical surface expand as distance increases?  Sketch a graph predicting how intensity will drop off with distance.  Now test your intensity versus distance model.

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 measure this intensity as a function 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 position scale on the optical rail measures the position of the sensor's base, not the actual detector inside. How might a systematic offset between the sensor base and the actual detector distort your data at close distances vs. far distances?
How will you determine or account for this offset?"

• 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.
• Design a sampling strategy (distance range and number of measurements) that gives you confidence in testing your intensity vs. distance model.
• In Excel, produce a table with the following headings.

• Move the sensor back in steps and record the measured intensity I for each sensor base position d_sb in the table for successive base positions.  When you are done taking data, close the Capstone program.
• Produce a plot of I - I_B versus the function of distance from your model.  If you model is correct, then this plot should show a straight line. 
• Label the axes of your plot.  Paste the plot into your journal.

Experiment 1 Deliverables: (to be included in the your journal)

• Visuals: 
  Your plot of I - I_B versus the function of distance from your model
• Analysis:
  State your intensity versus distance model.
  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

• Put two polarizers with their transmission axes at 90^o (crossed).  No light is transmitted.

If you place a third polarizer BETWEEN the two crossed polarizers, what do you predict will happen to the transmitted light intensity?
(Will it stay zero, decrease further, or increase?)

• Observe!  Model the electric field vector direction to explain your observation..

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

Experiment 2:

An incident wave has electric field amplitude E₀.  When it passes through a polarizer whose transmission axis makes an angle θ with the direction of E₀, what is the component of the electric field along the transmission axis?   Since intensity is proportional to E² derive a mathematical model for the ratio I(θ)/I₀.  This is called the Law of Malus.

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 determine the ratio I(θ)_transmitted/I₀.

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 (I -I_B/(I₀- I_B), 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/(I₀- I_B) versus angle (rad).  Label the axes.

Experiment 1 Deliverables: (to be included in the your journal)

• Visuals:  Your plot of(I -I_B/(I₀- I_B) versus angle (rad),
• Analysis: 
  Does your plot agree with what you expect from your mathematical model for the ratio I(θ)/I₀?
  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.  If a skeptic looked at your graph and claimed that light intensity is simply a linear function of angle between 0^o and 90^o, how would would you use your experimental results with their uncertainties to prove them wrong?

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:

Challenge:  You are an optical engineer designing polarized sunglasses to minimize glare from reflective surfaces.  Using the provided glass slide, laser, and polarizers, how can you determinethe refractive index n of the glass without measuring angles inside the glass?

Do the experiment.

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.
• 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.

Convert your journal into a lab report.

Name:
E-mail address:

Laboratory 6 Report

• 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 in your journal.
• Add a summary 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.