Turning Points Tutorial 3 – Is light a Wave?

 Contents

Isaac Newton (1642 – 1727) did many of the early experiments on light in the Seventeenth Century.  His argument was that light was a stream of particles.  This was nothing new; the Ancient Greek philosopher Democritus had proposed that objects were visible because of the swarm of particles that they put into the air.

Newton’s evidence was that:

• Objects cast sharp shadows; if they were a wave, the shadows would be fuzzy;

• Light passed through a vacuum; there was no material for a wave to propagate through.

His assumption was that particles travelled at a constant velocity except when near the boundary between two substance when unbalanced forces act on them.

In reflection the velocity perpendicular to the surface was reduced to zero, then increased to the original value in the opposite direction.  The velocity component parallel to the surface was unchanged.

In refraction the velocity perpendicular to the surfaces was increased by an attraction force.  The velocity component parallel to the surface was unchanged.  The light ray was bent towards the normal.

 Question 1 What happens to the resultant velocity as a result of the change that Newton proposed?  Is it consistent with what you know about the speed of light in a material?

The splitting of white light into the colours of the rainbow was explained by the difference in forces on the particles of different colours.

There are other limitations:

• The theory could not explain partial reflection or refraction.

• It could not explain interference.

• It seemed that there was both attraction and repulsion at some boundaries.

Another problem is that if there is an attractive force on the perpendicular movement, the path is not the straight line that we observe, it's a parabola, just like in projectile motion.

### Light as a Wave

At the same the same time as Newton, a Dutch physicist Hans Christiaan Huygens (1629 – 1695) proposed that light was a wave.  His view was prompted by the observation that beam of light cross each other without scattering.  If they were particles, there would be collisions between the beams.

His assumption was that light waves spread in all directions at a constant speed in a material called ether.  Ether permeated everything including a vacuum.

Huygens (pronounced “Harkens”) proposed models that consisted of plane wavefronts which consisted of secondary wavelets.  We tend to think of light passing as rays.  A ray describes the direction of travel of a light wave.  The way that Huygens describes light was as a set of plane wavefronts.  The wave fronts were at 90 o to the ray:

Huygens had observed that a a disturbance at single point source resulted in circular propagation of the waves:

In his principle he said that wavefronts were produced by many sources producing secondary wavelets.  A plane wavefront was produced from a line of point sources each producing secondary wavelets:

Only a few sources are shown here.  The wavefront would not be perfectly straight.  If there were lots of sources, the wavefront would be straight.  On the wavefront, secondary sources produce more wavelets to make another wavefront.

The same principle can be applied to curved wavefronts:

Huygens' Principle can be applied to reflection, refraction and diffraction.

The mechanism for reflection is like this:

• Wavefront 1 reaches point A.

• A wavelet from A starts to spread out.

• When the incident wavefront reaches B, the secondary wavelet from A has reached D, giving a new wavefront 2.

• Geometry can be used to show that the wavefronts make equal angles to the boundary, so that angle of incidence = angle of reflection.

The behaviour of the wavelets is shown in the picture below:

 When a wave is reflected, its phase changes by 180o .  How do you think this diagram is consistent with this observation?

Huygens explained refraction in a similar way

• Wavefront 1 reaches A.

• Wavefront from A starts to spread out.

• When incident wavefront reaches B, secondary wavelet from A has travelled a shorter distance to reach D.

• It gives a new wavefront 2.

• As a result the wave path bends towards the normal.

The diagram below shows the idea with the secondary wavelets:

Image from Arne Nordman, Wikimedia Commons (adapted)

His theory showed that the wave speed in the material was less than the wave speed in air.

 Question 3 Is this theory of refraction consistent with what you know already about refraction?

These observations are very similar to what we see when we study water waves.

Huygen’s theory did not discuss ideas of frequency and wavelength.  Light was though to emitted in pulses of energy.  There was no mathematical theory of continuous waves.  Nor had diffraction of light been noticed.

Although the wave behaviour of light was supported by many eminent scientists, it was rejected out of hand by Newton, who was the pre-eminent scientist with a considerable reputation.  Newton was not a pleasant man, cantankerous and desperately self-opinionated (Reminds you of somebody?).  Anyone who stood up to him risked having his work and character ridiculed.  That happened to Huygens, whose work remained overlooked for many years.  Also waves could not pass through a vacuum, so it was thought.  However on the continent, Huygen’s theory carried more weight.

There was little evidence either way and the debate ran on for many decades until the Nineteenth Century, until Thomas Young (1773 – 1829) performed his Double Slit experiment in 1801.  The details and quantitative treatment are given in Waves Tutorial 7.  You may wish to revise this.

 Question 4 Why was the wave nature of light slow to catch on?

Huygens' construction can also be used to explain diffraction:

The secondary wavelets come from the sources that are in the gap.  Wavefronts form along the corresponding secondary wavelets.  At the ends, the wavefront is curved, following the pattern of the circular secondary wavelet.

Huygens' construction explains how light can be propagated as a wave.  It still provides a good foundation for classical optics, although it is a static model, rather than dynamic model.  It provides a snapshot, rather than video, of the propagation.  In those days, the wave equation had not been worked out.

### Young’s Double Slits

In this experiment, Thomas Young demonstrated interference.  Part of the problem of demonstrating interference using two light sources is that getting coherent waves is impossible.  However if the ray from one source is split into two, by its nature, the ray consists of coherent waves.  Also getting pure monochromatic light was not easy, even with coloured filters.

 What is meant by coherent waves?

Nowadays it's very easy with a laser, which always gives out coherent monochromatic light.

In his day Young could only use a dim light source such as a candle or oil lamp. However the effect could be seen convincingly, and the experiment became a turning point in the debate between those who considered light as a wave.  There was no way that it could be explained by particles.  On the other hand it could be explained easily by wave theory.

• Light waves reach the screen after travelling different paths;

• At various places across the screen the waves are in phase or out of phase.

• Waves that are in phase add up to give a bright fringe; waves out of phase cancel out to give a dark fringe.

Although this was clearly a wave phenomenon, there was some delay before it was whole-heartedly accepted, which happened when a good mathematical argument was worked out.  Even then not all were convinced.

In 1850 the speed of light was measured in air and in water.  The speed of light in water was found to be lower than that in air, which:

• gave the answer predicted by the wave theory of refraction...

• ...and contradicted the particle theory.

Then the particle theory was finally abandoned in mainstream Physics thinking.

 Question 6 What made physicists believe that light was a wave rather than a particle?

### Electromagnetic Waves

In 1865 the theoretical physicist James Clerk-Maxwell (1831 – 1879) predicted that an oscillating electric field would cause a magnetic field to oscillate and vice versa.  By dint of rigorous mathematical analysis he predicted that the waves would propagate as a transverse wave and gave a formula for their speed.

• m0 (pronounced "mu-nought") is the Physics code for permeability of free space.  It is a constant and has a value of 4p × 10-7 H m-1.  It an important component in the mathematical analysis of magnetic fields and induction.

• e0 - (pronounced "epsilon-nought") is the Physics code for the permittivity of free space.  It is a constant and has the value 8.85 × 10-12 C2 N-1 m-2.  It is an important part of electric field phenomena.

 Question 7 Show that:   is about 3 × 108 m s-1.

It had been discovered in 1831 that a changing magnetic field always induced a voltage.  It would be reasonable to suppose that there would be an electric field associated with this voltage.  Maxwell also considered that it would be reasonable to say that a changing electric field would induce a magnetic field, which in turn would produce a changing electric field and so on.  From this he concluded that the electromagnetic wave where the electric field and the magnetic fields are at right angles to each other.

The diagram above shows:

• a transverse wave

• with an electric field vector

• and a magnetic field vector at right angles.

Electromagnetic waves can be polarised.  When the electric field vector is vertical, the wave is vertically polarised; when it is horizontal, the wave is horizontally polarised.

The electromagnetic wave remained a theoretical concept until their existence was demonstrated by a German Physicist Heinrich Hertz (1857 – 1894).  He set up this lethal looking apparatus (there was no Health and Safety at Work Act at the time):

• The induction coil produces a very high voltage.

• The electric field strength between the spheres is strong enough for the insulating properties of air to break down (approximately 3000 V mm-1).

• The effect was intensified if the radiation was reflected using parabolic reflectors on both the transmitter and receiver,

• When the spark jumps, it generates a spark that produces a high frequency damped electrical oscillation.

 Question 8 What would the charge time graph for the electrical oscillation look like? ( Hint: It’s like a spring)

The high frequency oscillations induce a voltage in the loop which was sufficient to cause a small spark to jump.  The spark could be made more powerful if the loop was put at the focal point of a concave mirror.  If he put the loop on its side, the effect was not seen at all, indicating that the waves were polarised.  The two pictures below explain in simple terms why the polarisation happens.

The E field exerts a force F = Eq on the electrons, making them move up and down.  An emf is induced.  Also, the magnetic component of the waves is at 90 degrees to the aerial.  An emf is induced by Faraday's and Lenz's Laws.

If the aerial is moved through 90 degrees, the movement of electrons remains up and down, but this movement is 90 degrees across the wire.  Therefore no emf is induced.  Additionally the B-field component is parallel with the wire.  F = BA cos 90 = 0.

 The alternating wave is not sinusoidal.  The EMF induced by the induction coil rises and falls exponentially, as current in an inductor rises and falls exponentially.  The reasons for this are not on the syllabus.  If we measure the output from the receiver with a CRO, it would be very messy as there is sparking.

Another experiment that Hertz carried out was study the standing wave nature of radio waves.  He moved his detector between his transmitter and a flat metal sheet.  He noticed that there were points at which the sparking was non-existent, or very weak.  The weak points coincided with the nodes of a standing wave pattern.  You have probably seen a similar experiment carried out using 3 cm waves.

Hertz went on to work out the frequency on the assumption that the effect was due to electrical resonance.  He also set up standing waves and found the wavelength between nodes.  This allowed him to determine the speed of the waves, getting a very similar result to what Maxwell had predicted in his theoretical calculations.  However Hertz could not think of any earthly use for this result, other than that it was an interesting physics curiosity.

This experiment formed the basis for experiments by Guillermo Marconi, the son of an Italian Count, into wireless telegraphy.

It had been clinched.  Light was a wave.

It is easy to dismiss the early ideas as ludicrous.  Modern physicists have the truths based on years of painstaking research by the world’s most eminent physicists, which are handed down from generation to generation.  Each generation of teachers has its set of books on which their material is based; the style will change, but the essential truths will not.  The early physicists had none of these; their work was based entirely on observation from pretty primitive technology.  It is easy to pick up misconceptions where there is no bedrock of underlying truth.  The theories produced were presented in total good faith.  The early physicists were men of integrity, even if they were at times head-strong.  Obnoxious though he was, Newton produced the laws on which space flights are based today.

Contrast that to some scientists today who, for whatever reason, have sacrificed integrity in order to fulfil an unrealistic target set by a manager, or worse still to make a quick buck.