## Studio Session 7

### 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 measure the intensity of a light wave as a function of distance from the source and you will investigate various polarization effects.

Equipment Needed:

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

Note:  The different experiments require different components on the rail.  When you are finished with your experiments, please return the components to the rail as shown in the picture.

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 E2max is proportional 1/r2, or Emax 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.

• Mount the light bulb and the sensor onto the optical rail.  Remove all other components from their post holders, but do not remove the post holders from the rail.  On the sensor set the gain to 1.
• Adjust the height of the sensor so it is at the same height as the filament of the light bulb.  (Use a ruler and measure or bring them close together.)  Make sure the lamp and sensor face each other. Then tighten their posts in the post holders.
Always loosen and tighten the screws on the post holders to make adjustments.
• Plug the 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.  Chose a sample rate of 20 Hz.
• 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, and shield your sensor as much as possible from the light of the bulbs from other groups.
• Record the background intensity IB in units of %.
• Turn on the light bulb.
• The maximum light intensity the sensor displays before it saturates is ~95%.  Move the sensor away from the bulb until the displayed intensity is ~80%.
• Record the location, dsb, of the sensor base on the optical rail.
• Measure the actual distance, dact, between the filament tip and the sensor window.  Record this distance.
• Calculate the offset distance doff = dsb - dact.
• Open Microsoft Excel.  Create a table in Excel.
 dsb I r = dsb - doff 1/r2 I - IB
• Move the sensor back in 2 cm steps and record the measured intensity I for each sensor base position dsb in the table for 12 successive base positions.  When you are done taking data, click Stop.
• Create calculated columns, r = dsb - doff, 1/r2, and I = I - IB.  I - IB is the measured intensity I at a distance r = dsb - doff from the source.
• Produce a plot of I - IB 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

Itransmitted = I0 cos2θ.

 Polarizers with parallel transmission axes Polarizers with perpendiculartransmission 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.  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.
• Light from LCD screens is polarized.  Look through a polarizer at the screen of your laptop or cell phone.

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 Itransmitted = I0 cos2θ.  This is called the Law of Malus.

• Tighten down the light sensor at ~ 80 cm on the rail.
• In the Capstone program, keep the setup of the light sensor from experiment 1.  Re-measure the background intensity IB.
• Your light source for this experiment is a diode laser.  Mount it onto the optical rail as shown at ~40 cm.
• 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.)
• Insert the two polarizers with their transmission axes aligned vertically between the laser and the light sensor.  The polarizer holders should have their dial sides facing away from each other.  Make sure the polarizer disks are perpendicular to the laser beam.  Tighten their post in the post holders.  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.

 angle (deg) I angle (rad) I - IB I0*cos2(angle)
• 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 10o steps.  For angles between 0 and 180o in 10o steps measure and record the intensity I in the table.
• When you are done taking data click Stop.
• Create calculated columns I - IB 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 - IB 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 θB, where tanθB = n2/n1.  The Brewster angle for reflecting off glass is between 50o and 60o.

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 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 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 90o, so that its transmission axis is horizontal.  It now blocks vertically polarized light.
• Using the rotation stage, rotate the slide approximately 55o.  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 tanθB = nglass/nair = nglass, since nair = 1.
• Is your value for nglass 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?