Lab 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 lab you will investigate various polarization effects.

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.


Open the polarization lab simulation.  You are presented with a He-Ne laser, an optical breadboard and several optical components.  The components can be dragged to different positions on the breadboard and the components can snap to the holes on the breadboard which have a spacing of 1 unit = 2.5 cm.  The screen is 4 units wide and 2 units high and the lines on the screen are spaced by ½ unit.  Clicking anywhere on the breadboard you can rotate and zoom the view. A transparent viewer can help you align the beam.  All components can be translated and rotated, and the post holders can be raised and lowered with the mouse.

The He-Ne laser beam (λ = 633 nm) is unpolarized.  You have 3 (ideal) linear polarizers and a power meter with a Bluetooth connection to a digital readout to monitor the beam intensity.  You can also monitor the intensity of the laser beam on a screen (corrected for the average response of the human eye to light).  The polarizers are mounted in a rotation stage.  The transmission axis of the polarizers is horizontal when the rotation stage reads zero.  You can explore what happens to the transmitted intensity if you rotate a third polarizer between two crossed polarizers and you can verify the Law of Malus.  You can also reflect the laser beam off a glass slide and explore polarization by reflection.  The back of the glass slide is painted black to absorb the transmitted portion of the beam.  The slide is made of high-index of refraction glass, you can measure the index of refraction by finding the  the Brewster angle.

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.

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



Spend a few minutes exploring what happens to the intensity of the beam spot on the screen as you pass the beam first through one and then through two polarizers.  Observe the change in transmitted light intensity as either of the polarizers is rotated.  This combination acts as a "light valve."


Place a third polarizer between two crossed polarizers and rotate the transmission axis of the third polarizer while observing the intensity of the beam spot on the screen.

Experiment 1:

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.


Use the setup shown in the picture above.  It uses the power meter to monitor the beam intensity.  You can increase the spacing between the components to make it easier to rotate the polarizers.  Start with the transmission axes of both polarizers horizontal (zero degrees).  If necessary, adjust the height of all components so that the beam falls onto the power meter and the mater reads 0.75 mW.  (Note:  The readout position is fixed, you cannot drag it around,) 

After the laser light has passed through the polarizers, it is ~100% polarized along the horizontal direction, since the transmission axis of each polarizer is horizontal.

In Excel create a table.  You can download the first row here.

angle (deg) angle (rad) I (mW) I0*cos2(angle)

imagePolarization 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.  For a air-glass boundary, tanθB = nglass.  The Brewster angle for reflecting off glass is between 55o and 60o.

Experiment 2:

You will reflect the laser light off a glass slide  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, for example if sunlight is reflecting at a low angle off a lake, 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, as for our glass slide, 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 slide and find the Brewster angle.



Convert your log into a lab report.

E-mail address:

Laboratory 6 Report

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