Electromagnetic wave theory & the speed of light

The work of Fizeau, Foucault, Hertz and Maxwell contributed to our understanding of the nature of light.

Fizeau measured the speed of light in air. Foucault confirmed that light travels faster in air than in water. Hertz measured the speed of radio waves in air. Maxwell developed a theory that was used to obtain the speed of light.

Discuss how the work of these four scientists contributed to our understanding of the nature of light.

In your answer you should refer to:

• the two pre-1800 models for the nature of light

• the predictions that these models made about the speed of light

• Maxwell’s theory

• the significance of the measurements made by Fizeau, Foucault and Hertz.

Do not include any experimental details in your answer.

Hertz did an experiment to determine the speed of radio waves.

Describe this experiment.

In your answer you should:

• include a labelled diagram

• state the measurements that were taken

• describe how the data were used to determine the speed of radio waves.

An electromagnetic wave is propagating through space.

Figure 3 shows the variation of the magnetic flux density of the wave with distance. The magnetic field is in the xz plane. The y-axis is at right-angles to the xz plane.

Draw and label on Figure 3:

• the corresponding electric field

• the direction of propagation of the wave.

Which scientist proposed the electromagnetic wave model of light?

Tick () one box.

Another theory of the nature of light was proposed by Isaac Newton.

Describe how Newton’s theory was used to explain the refraction of light as it moves from air into glass.

Describe a demonstration using visible light that can be performed in a school laboratory to show that Newton’s theory is not correct.

Figure 5 shows the arrangement used by Fizeau to determine the speed of light.

The toothed wheel W is rotated and the reflected light from a distant mirror M is observed.

The speed of light is calculated from the equation

where d is the distance from W to M and n is the number of teeth on the rotating wheel W.

State what f₀ represents in the equation.

The experiment is attempted using a rotating wheel with 720 teeth that can be rotated at up to 620 revolutions per minute. The distance between W and M is 8.5 km.

Deduce whether the speed of light can be determined with this particular arrangement.

The determination of the speed of light took on extra significance when Maxwell derived the wave-speed equation

State how ε₀ and µ₀ are related to the types of field in the wave.

µ₀

In 1864, James Clerk Maxwell published a theory that included an equation for the speed of electromagnetic waves in a vacuum.

Show that Maxwell’s theory agrees with the accepted value for the speed of light in a vacuum. Use information from the Data and Formulae Booklet in your answer.

Between 1886 and 1889, Heinrich Hertz completed a series of experiments in an attempt to verify Maxwell’s theory. Figure 3 shows a simplified arrangement similar to the one used by Hertz in one of his experiments.

T is a radio wave transmitter with an aerial consisting of two vertical metal rods. D is a detector that uses a conducting loop aerial.

T is switched on so that an oscillating current is produced in the metal rods. An emf is detected in the conducting loop aerial.

Explain this experiment with reference to Maxwell’s model of electromagnetic waves.

In a different experiment Hertz used stationary waves to determine the speed of radio waves. Figure 4 shows an experimental arrangement similar to the arrangement Hertz used.

Stationary waves are produced between the fixed transmitter and the fixed metal reflector.

In one experiment the distance between the transmitter and reflector is about 12 m and the transmitter frequency is 75 MHz.

Deduce whether this arrangement can be used to measure the speed of electromagnetic waves suggested by Maxwell’s equation.

Newton used a corpuscular theory of light to explain reflection.

Figure 2 shows how corpuscles would reflect from a horizontal surface.

What happens to the horizontal and vertical components of the velocity of the corpuscles, according to the theory, when they are reflected?

Tick (✓) one box.

Newton used the corpuscular theory to explain the refraction of light at an interface between air and water.

Huygens used the wave theory to explain the refraction of light at the interface.

Discuss the evidence that led to the rejection of Newton’s corpuscular theory.

In your answer you should include

• how each theory explains refraction

• how experimental evidence led to the acceptance of the wave theory.

Light is now known to behave as an electromagnetic wave.

Describe a plane-polarised electromagnetic wave travelling through a vacuum. You may wish to draw a labelled diagram.

Figure 2 shows a modern version of the apparatus used by Hertz to investigate the properties of electromagnetic waves. Electromagnetic waves are continuously emitted from a dipole transmitter. The electromagnetic waves are detected by a dipole receiver. An oscilloscope is used to display the amplitude of the detected signal at the dipole receiver.

Figure 3 shows the same apparatus when the dipole receiver has been rotated through an angle of 90º

Sketch a graph on Figure 4 to show how the amplitude detected by the dipole receiver varies with angle of rotation as the receiver is turned through 360° Start your graph from the position shown in Figure 2.

Maxwell derived the equation c =c = for the speed c of electromagnetic waves, where is the permeability of free space and ₀ is the permittivity of free space.

Explain, using a suitable calculation, why this equation led to the conclusion that light is an electromagnetic wave.

The following observations are made.

A When the speed of rotation is low the observer sees the light returning after reflection by the mirror M.

B When the speed of the wheel is slowly increased the observer continues to see the light until the wheel reaches a certain speed. At this speed the observer cannot see the light.

Explain these observations.

Observation A

Observation B

Table 1 shows data from Fizeau’s experiment at the instant when observation B is made.

It can be shown that the speed of light c is given by the equation

c = 4 dnf

Discuss whether the data in Table 1 are consistent with the present accepted value for the speed of light.

The speed of the wheel is further increased.

Deduce the value of f when the observer would next be unable to see light returning from the mirror.

Explain how the nature of light is implied by Maxwell’s theory of electromagnetic waves and Fizeau’s result.