o Aim of the lecture Introduction of Waves

water as a model Radio

Light representation with rays refraction reflection

o  Main learning outcomes familiarity with

Waves Radio Light

Lecture 11

Maxwell’s Equation’sHave more solutions thanconsidered so far in course.

In particular it is possible tohave free space solutions(no sources, ie no charges)

For example:

And k is 2/l where l is wavelength

In this course we will not study such solutions in detail, howeverthese are wave solutions and are very important. What is describedby the equations below is a radio wave propagating in the z direction.

We will return to the radio wave.

What IS a wave??

Consider first a wave in water

Notice that the buoy doesnot move across the surfaceit only moves in a small circle.

What is moving fromleft to right across thepicture is ‘energy’. Nothingphysical is translating, butenergy is being moved fromleft to right by the collectiveaction of the water molecules.

This is a ‘transverse surface wave’

Transverse means that the motion of the medium is perpendicularto the direction of energy transportSurface means that it is at the boundary between two media

Water waves demonstrate most of the phenomenaof waves, so we will return to them.

o Radio waves are also transverse, but they are 3D,They do not require a surfaceThey also do not require medium (!!)

(It was consideration of this that led Einstein to E=mc2 )o The equations which describe water waves are ‘almost’ the same as those for radio waveso Not identical.

Sound is also a wave

o It is a 3D waveo But NOT transverse,o Sound is a ‘longitudinal’ waveo It is a compression wave in air

The air molecules vibrate back and forth, but do nottranslate on average. Energy is transferred.

o Water waves and sound waves both have a physical medium

o There would be no sound and no water waves without a medium.

Water, oil, all liquids will exhibit ‘water’ waves

Water, oil, all liquids, all solids, all gases will exhibit sound waves

How well they propagate will depend on which medium.

o Radio waves however propagate happily in vacuum and why not? – electric and magnetic fields exist in vacuum these ‘fields’ are representations of a phenomena, they are not ‘real’

oRadio waves are just one form of Electromagnetic wave.

oThere are many kinds of e-m waveRadioMicrowaveInfra redVisible lightUltra violetX-rayGamma Ray

The ONLY difference between these is the frequency, , ofthe oscillation.

These e-m waves have many properties, which depend on theirfrequency, as shown in the diagram:

Frequency

Wavelength

For any wave, v = f

Where v is the velocity of energy propagationf the frequency is the wavelength

For e-m waves v = c in vacuum

c = 3 x 108 m/s

Note that this is classical electromagnetism

The very best theory is called QED - Quantum Electrodynamics This is a VERY accurate theory, good to 1 part in 1010

The most obvious thing added by QED isQuantisation Radio, light,… propagate as ‘particles’, which are little bundles of energy

The waves cannot transmit any quantity of energy, but onlyin fixed sized bundles.

However the bundle size is extremely small, so we do not noticethis in everyday life. [ ~ 2 x 10-19 Joules for visible light]

We do not need to think about this anymore in this course.

Einstein received his Noble Prizefor his work on quantisation of electromagnetic radiation

(NOT for E=mc2) or general relativity

Speed of Light

The speed of a light wave invacumm is always the same, it is v = 3 x 108 m/s

•In fact this is a universal speed limit, nothing can travel faster than this speed.•Light happens to have the correct properties so that it can travel exactly at the speed limit.

Exact value = 299,792,458 m/s

This really is EXACT, it has no error at all, because the sizeof a metre is now defined in terms of this universal speed limit

Remember that there is a universal speed limitwhich nothing can go faster than,

It so happens that light can go at this speed

Don’t make the mistake of half the people on the planet andimagine that light has anything to do with the speed limit. It does not!

Light travels at the speed limit, it does not create the limit.

v = c/n

Where c is speed in vacuumand n is a constant which dependson the type of medium.

When light is travelling through something otherthan vacuum, it does not travel as the universal speed limit

It travels more slowly.

The speed reduction is defined in terms of a factor, called

the refractive index

Properties of Waves

Waves exhibit the phenomena ofReflection, Refraction, Diffraction, Dispersion, Interference

These are the properties of most wavesOften easier to envisage in water on a surfaceBut apply to all, including 3D waves

There are additional properties, such as polarisation, which are not exhibited by water waves, but we will notbe talking about these.

The equation earlier:

is describing the magnetic field in a circularly polarised waveIf you take a more advanced course, you will learn about this andother exciting features of e-m radiation.

Reflection.

Waves incident on a surface, such as the side of a swimming poolwill reflect off and keep travelling in a new direction.

The arrowed lines are called ‘rays’ and they show the direction oftravel of the energy associated with the wave

In reflection, angle of incidence = angle of reflection

Refraction.

If there is a boundary between shallow and deep water, The speed of waves will change (slower in shallow water) If the boundary is at an angle to the ray direction, then

the wave-front must change direction as the wave will slow down in the shallow water at different times

The waves are getting closer together towards theleft of the picture, this is caused by refraction.

The relationship between the incident and refracted directionsis called ‘Snell’s Law’

This is usually done forLight rays in glass, ratherthan water waves, but theprinciple is the same.

The speed of a light wave inglass is

v = c/n

Where c is speed in vacuumand n is a constant which dependson the type of glass

Snell’s Law:

sin(1) v1 n2

sin(2) v2 n1

= =

Ray direction bends TOWARDS the normal in the slower medium

Snell’s Law:

sin(1) v1 n2

sin(2) v2 n1

= =

From inside the slower medium,(usually denser), there is an anglebeyond which the light cannot getinto the low speed medium anymore

All the light then reflects, none refracts

This is called the Brewster Angle

The boundary acts like a mirror

Fibre optic communication works like this: the light is launched into the fibre at an angle which means it keepsbouncing along the inside of the fibre, none can get out.

It is done this way because the efficiencyof bounce can be very high, almost no energyloss per bounce (unlike a normal mirror)

But be cautious, it is a bit morecomplicated than this, we wouldneed to talk about polarisationto discuss refraction properlyin the case of light.

Fibre optics is an Engineering TopicA huge subject just in itself

One final wave for the lecture: