Electro magnetic theory

Plane waves reflection refraction and polarization

joint effort by

Dinesh raj

Rohit

Kanishth

Prashanth

Awadesh

Consists of

Plane waves Properties Reflection Refraction Total internal reflection Polaraization Applications

Plane waves

A plane wave can be written as follows:

Here A represent the E or B fields, q=i,r,t and j=x,y,z

So this is a representation of the waves that is valid in all three cases, i.e. the incoming, the reflected and the transmitted wave Boundary conditions

The most importent condition at the boundary is the existence of continuity

This gives us that the tangential component of the argument in the wave-equations have to be equal, i.e. the waves are in the plane of incidence

)(Re wtiqj

qj

q

eaA rk

Electromagnetic Waves

It consists of mutually perpendicular and oscillating electric and magnetic fields. The fields always vary sinosidally. Moreover, the fields vary with the same frequency and in phase (in step) with each other.

The wave is a transverse wave, both electric and magnetic fields are oscillating perpendicular to the direction in which the wave travels.  The cross product always gives the direction in which the wave travels.

Electromagnetic waves can travel through a vacuum or a material substance.

All electromagnetic waves move through a vacuum at the same speed, and the symbol c is used to denote its value. This speed is called the speed of light in a vacuum and is:

The magnitudes of the fields at every instant and at any point are related by

E B

                                                               

                                                               

                                                               

                                                               

Properties of the Wave

Wavelength λ is the horizontal distance between any two successive equivalent points on the wave.

Amplitude A is the highest point on the wave pattern.

Period T is the time required for the wave to travel a distance of one wavelength. Unit is second.

Frequency f : f=1/T. The frequency is measured in cycles per second or hertz (Hz).

Speed of wave is v=λ/T= λf

                                                                                                                                                                                    

The Speed of Light

All electromagnetic waves travel through a vacuum at the same speed, which is known as the speed of light c=3.00×108 m/s. 

All electromagnetic waves travel through a material substance with the speeds less than the speed of light in vacuum c=3.00×108 m/s. The waves with different wave lengths may have different speeds in a material substance.

In 1865, Maxwell determined theoretically that electromagnetic waves propagate through a vacuum at a speed given by 8

0 0

13.00 10c

(m/s)

Reflection and refraction

Why are we able to see ourselves from mirror?

The incident ray, the reflected ray, and the normal to the surface all lie in the same plane, and the angle of reflection θr equals the angle of incidence θi:

r i

Law of refraction

A refracted ray lies in the plane of incidence and has an angle θ2 of refraction that is related to the angle of incidence θ1 by:

the symbols n1   and n2    are dimensionless constant, called the index of refraction

ii

cn

v

Dispersion

The index of refraction encountered by light in any medium except vacuum depends on the wavelength of the light. The dependence of n on wavelength implies that when a light beam consists of rays of different wavelengths, the rays will be refracted at different angles by a surface; that is, the light will be spread out by the refraction. This spreading of light is called chromatic dispersion,

                                                                                                            

                                                                                                                                                                                                                

•The index of refraction n in the different materials is different for the same wave length of lights.•The index of refraction n in the same materials is different for different wave length of lights.

A phenomenon in which some of the light that is travelling from one medium into another is reflected & some is refracted at theboundary between two media.

Total Internal Reflection

optical fibres

core (made of glass)

cladding (made ofanother type of glasswith a lower refractive index)

Total Internal Reflection

    

                                                                                                                                                                                                                                      

                                                                                                                    

we look at the phenomenon of total internal reflecection whichis the opposite of the one just considered in that no energy is transmitted across aninterface under appropriate conditions.

•Total internal reflection •

• is the phenomenon in which incident light is not refracted but is entirely reflected back from the boundary. It happens only when light travels from a medium in which its speed is lower to a medium in which its speed is higher. The amount of reflection compared with the amount of refraction depends on the angle of incidence.

Polarization Polarization is a characteristic of all transverse

waves. Oscillation which take places in a transverse

wave in many different directions is said to be unpolarized.

In an unpolarized transverse wave oscillations may take place in any direction at right angles to the direction in which the wave travels.

Direction of propagation of wave

Polarization of Electromagnetic Waves

Any electromagnetic wave consists of an electric field component and a magnetic field component.

The electric field component is used to define the plane of polarization because many common electromagnetic-wave detectors respond to the electric forces on electrons in materials, not the magnetic forces.

Polaroid

A Polaroid filter transmits 80% or more of the intensity of a wave that is polarized parallel to a certain axis in the material, called the polarizing axis.

Polaroid is made from long chain molecules oriented with their axis perpendicular to the polarizing axis; these molecules preferentially absorb light that is polarized along their length.

Polarizing axis

Polarization by Reflection Unpolarized light can be polarized, either partially or

completely, by reflection. The amount of polarization in the reflected beam

depends on the angle of incidence.

Brewster’s law It is found that experimentally when the

reflected ray is perpendicular to the refracted ray, the reflected light will be completely plane-polarized.

Reflectedray

Incidentray

o90

p

r

p1n

2n

Polarizing angle (Brewster’s angle)

The angle of incidence at which the reflected light is completely plane-polarized is called the polarizing angle (or Brewster’s angle).

By Snell’s law, rp nn sinsin 21 Since and

ppo

r cos)90sin(sin

Then we get

1

2tann

np

90rp

Polarization by Scattering (1)

When a light wave passes through a gas, it will be absorbed and then re-radiated in a variety of directions. This process is called scattering.

Unpolarizedsunlight

Gas molecule

Light scattered at right anglesis plane-polarized

O

y

z

x

Polarization of Scattered Sunlight

x

y

z

O

E

Polarization by Refraction

When an incident unpolarized ray enters some crystals it will be split into two rays called ordinary and extraordinary rays, which are plane-polarized in directions at right angles to each other.

Double Refraction

When light is refracted into two rays each polarized with the vibration directions oriented at right angles to one another, and traveling at different velocities. This phenomenon is termed "double" or "bi" refraction.

Applications…..

Electric field of EM wave produces a current in an antenna consisting of straight wire or rods.

Changing magnetic field induces an emf and current in a loop antenna.

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