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.

image Equipment Needed:

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.

dsb I r = dsb - doff  1/r2 I - IB


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 with the three pieces of linear polarizing material provided to you in an envelope.


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.

In Excel create a table.

angle (deg) I angle (rad) I - IB 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.  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.

Convert your log into a session report, certify with you signature that you have actively participated, and hand it to your instructor.