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’s Have more solutions than considered so far in course. In particular it is possible to have 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, however these are wave solutions and are very important. What is described by 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 does not move across the surface it only moves in a small circle. What is moving from left to right across the picture is ‘energy’. Nothing physical is translating, but energy is being moved from left to right by the collective action of the water molecules. This is a ‘transverse surface wave’ Transverse means that the motion of the medium is perpendicular to the direction of energy transport Surface means that it is at the boundary between two media

Water waves demonstrate most of the phenomena of waves, so we will return to them. o Radio waves are also transverse, but they are 3D,  They do not require a surface  They also do not require medium (!!) (It was consideration of this that led Einstein to E=m  c 2 ) o The equations which describe water waves are ‘almost’ the same as those for radio waves o Not identical.

Sound is also a wave o It is a 3D wave o But NOT transverse, o Sound is a ‘longitudinal’ wave o It is a compression wave in air The air molecules vibrate back and forth, but do not translate 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 wave  Radio  Microwave  Infra red  Visible light  Ultra violet  X-ray  Gamma Ray The ONLY difference between these is the frequency, , of the oscillation.

These e-m waves have many properties, which depend on their frequency, as shown in the diagram: Frequency Wavelength For any wave, v = f Where v is the velocity of energy propagation f the frequency is the wavelength For e-m waves v = c in vacuum c = 3 x 10 8 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 The most obvious thing added by QED is Quantisation Radio, light,… propagate as ‘particles’, which are little bundles of energy The waves cannot transmit any quantity of energy, but only in fixed sized bundles. However the bundle size is extremely small, so we do not notice this in everyday life. [ ~ 2 x Joules for visible light] We do not need to think about this anymore in this course. Einstein received his Noble Prize for his work on quantisation of electromagnetic radiation (NOT for E=m  c 2 ) or general relativity

Speed of Light The speed of a light wave in vacumm is always the same, it is v = 3 x 10 8 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 size of a metre is now defined in terms of this universal speed limit Remember that there is a universal speed limit which 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 and imagine 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 vacuum and n is a constant which depends on the type of medium. When light is travelling through something other than 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 of Reflection, Refraction, Diffraction, Dispersion, Interference These are the properties of most waves Often easier to envisage in water on a surface But apply to all, including 3D waves There are additional properties, such as polarisation, which are not exhibited by water waves, but we will not be talking about these. The equation earlier: is describing the magnetic field in a circularly polarised wave If you take a more advanced course, you will learn about this and other exciting features of e-m radiation.

Reflection. Waves incident on a surface, such as the side of a swimming pool will reflect off and keep travelling in a new direction. The arrowed lines are called ‘rays’ and they show the direction of travel 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 the left of the picture, this is caused by refraction.

The relationship between the incident and refracted directions is called ‘Snell’s Law’ This is usually done for Light rays in glass, rather than water waves, but the principle is the same. The speed of a light wave in glass is v = c/n Where c is speed in vacuum and n is a constant which depends on the type of glass

Snell’s Law: sin(  1 ) v 1 n 2 sin(  2 ) v 2 n 1 = Ray direction bends TOWARDS the normal in the slower medium

Snell’s Law: sin(  1 ) v 1 n 2 sin(  2 ) v 2 n 1 = From inside the slower medium, (usually denser), there is an angle beyond which the light cannot get into 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 keeps bouncing along the inside of the fibre, none can get out. It is done this way because the efficiency of bounce can be very high, almost no energy loss per bounce (unlike a normal mirror) But be cautious, it is a bit more complicated than this, we would need to talk about polarisation to discuss refraction properly in the case of light.

Fibre optics is an Engineering Topic A huge subject just in itself One final wave for the lecture: