Chapter 33. Electromagnetic Waves

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Chapter 33. Electromagnetic Waves

• 33.1. What is Physics?      
• 33.2. Maxwell's Rainbow      
• 33.3. The Traveling Electromagnetic Wave,
  Qualitatively      
• 33.4. The Traveling Electromagnetic Wave,
  Quantitatively      
• 33.5. Energy Transport and the Poynting
  Vector         
• 33.7. Polarization      
• 33.8. Reflection and Refraction      
• 33.9. Total Internal Reflection      
• 33.10. Polarization by Reflection

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What is Physics?
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Maxwell's Rainbow





                                                                                                                                                                                                                                                                                                                                                          

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Sensitivity of the average human eye


                                                                                                 
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Electromagnetic Waves

                                                               

                                                               

                                                               

                                                               

• It consists of mutually perpendicular and
  oscillating electric and magnetic fields. The
  fields always vary sinusoidally. 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

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Properties of the Wave


                                                                                                                                                                                    

• Wavelength ? 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 f1/T. The frequency is measured in
  cycles per second or hertz (Hz).
• Speed of wave is v?/T ?f

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The Speed of Light

• All electromagnetic waves travel through a vacuum
  at the same speed, which is known as the speed of
  light c3.00108 m/s. 
• All electromagnetic waves travel through a
  material substance with the speeds less than the
  speed of light in vacuum c3.00108 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

(m/s)
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The Energy Carried by Electromagnetic Waves
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Poynting Vector

• The rate of energy transport per unit area in EM
  wave is described by a vector, called the
  Poynting vector

• The direction of the Poynting vector of an
  electromagnetic wave at any point gives the
  wave's direction of travel and the direction of
  energy transport at that point.

• The magnitude of S is

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Intensity of EM Wave
the root-mean-square value of the electric field,
as

                                           


                                             

• The time-averaged value of S is called the
  intensity I of the wave

The root-mean-square value of the electric field,
as

• The energy associated with the electric field
  exactly equals to the energy associated with the
  magnetic field.

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Variation of Intensity with Distance


                                                                                             

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Polarization

• A linearly polarized electromagnetic wave is one
  in which the oscillation of the electric field
  occurs only along one direction, which is taken
  to be the direction of polarization.

                                                                                           

• Polarized randomly, or unpolarized wave is one
  in which the direction of polarization does not
  remain fixed, but fluctuates randomly in time.

• Partially polarized wave

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Polarizing Sheet

• An electric field component parallel to the
  polarizing direction is passed (transmitted) by a
  polarizing sheet a component perpendicular to it
  is absorbed.
• one-half rule an unpolarized light pass through
  a polarizing sheet, the intensity I of the
  emerging polarized light is

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MALUS LAW
                                                                                              

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Example  
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Example
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Example

• What value of ? should be used in Figure, so
  the average intensity of the polarized light
  reaching the photocell is one-tenth the average
  intensity of the unpolarized light?

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Geometrical Optics

• Wave fronts the surfaces through all points of
  the wave that are in the same phase of motion are
  called wave fronts.
• Rays the radial lines pointing outward from the
  source and perpendicular to the wave fronts are
  called rays. The rays point in the direction of
  the velocity of the wave.

• Although a light wave spreads as it moves away
  from its source, we can often approximate its
  travel as being in a straight line. The study of
  the properties of light waves under that
  approximation is called geometrical optics

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Reflection and Refraction


                               

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The Reflection of Light

• Why are we able to see ourselves from mirror?

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LAW OF REFLECTION

• The incident ray, the reflected ray, and the
  normal to the surface all lie in the same plane,
  and the angle of reflection ?r equals the angle
  of incidence ?i

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Example

• Two plane mirrors are separated by 120, as the
  drawing illustrates. If a ray strikes mirror M1,
  at a 65 angle of incidence, at what angle ? does
  it leave mirror M2?

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Law of refraction

• A refracted ray lies in the plane of incidence
  and has an angle ?2 of refraction that is
  related to the angle of incidence ?1 by

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

• The index of refraction n 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.

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Dispersion


                                                                                                                                                                                                                


                                                                                                            
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Total Internal Reflection
    




                                                                                                                                                                                                                                                                                                                                                          
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Polarization by Reflection

• A ray of unpolarized light incident on a glass
  surface. The electric field vectors of the light
  has two components. The perpendicular components
  are perpendicular to the plane of incidence The
  parallel components are parallel to the plane of
  incidence. Because the light is unpolarized,
  these two components are of equal magnitude.
• The reflected light also has both components but
  with unequal magnitudes.
• When the light is incident at a particular
  incident angle, called the Brewster angle , the
  reflected light has only perpendicular
  components,