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					                   Electromagnetic
                        Waves


11,16 April 2007        PHYS 202: Chapter 24   1
                   Introduction to Waves

      A wave is a traveling disturbance and
      carries energy from place to place

      There are 2 basic types of waves:
             Transverse waves
             Longitudinal waves




11,16 April 2007           PHYS 202: Chapter 24   2
                      Transverse Waves

      In a transverse wave, the disturbance
      occurs perpendicular (transverse) to the
      direction of wave
      travel




      Examples:
             Waves in a string or rope
             Electromagnetic waves
11,16 April 2007            PHYS 202: Chapter 24   3
                    Longitudinal Waves

      In a longitudinal wave, the disturbance
      occurs parallel to the direction of wave
      travel




      Examples:
             Sound waves



11,16 April 2007           PHYS 202: Chapter 24   4
                   Anatomy of Vibration or Wave

      Amplitude: distance
      from midpoint to
      crest, or to trough
      Frequency f: number
      of vibrations per unit
      time
      Period T: time for one complete vibration,
      related to f by f = 1/T

      Frequency is measured in hertz (Hz)
      where 1 Hz = 1/s

11,16 April 2007              PHYS 202: Chapter 24   5
                   Wavelength & Wave Speed

      The distance between any successive
      identical parts of a wave is one
      wavelength, λ




      The speed v of a wave is the distance
      covered each period, or       λ
                                                  v
                                                       T
      Also         v=λf
11,16 April 2007           PHYS 202: Chapter 24            6
   Creation of Electromagnetic Waves

      Stationary charges create static
      electric fields, and oscillating
      charges create oscillating electric
      fields
      Charges moving with constant
      speed create static magnetic
      fields, and oscillating charges (or
      currents) create oscillating
      magnetic fields
      Thus oscillating charges create
      electromagnetic waves
             each consisting of mutually
             perpendicular and oscillating
             electric & magnetic fields
11,16 April 2007               PHYS 202: Chapter 24   7
                   Electromagnetic Waves




                                                   Simulation

      Electromagnetic (EM) waves
             are transverse waves
             can travel through a vacuum or a material
             substance
             all travel through a vacuum at the same
             speed c = 3.00×108 m/s, called the speed
             of light in a vacuum
11,16 April 2007            PHYS 202: Chapter 24                8
        Electromagnetic Spectrum
The EM spectrum is the entire range of
wavelengths (or frequencies) of EM waves,
including the visible spectrum




Simulation
                   Example: Visible Light Waves

      Find the range of wavelengths (in
      nanometers) for visible light in the
      frequency range between 4.0×1014 Hz
      (red light) and 7.9×1014 Hz (violet
      light)




      Answer:

11,16 April 2007              PHYS 202: Chapter 24   10
                      Visible Light




                   Wavelength in nanometers

      Different wavelengths (or frequencies) of light
      are perceived by the eye as different colors
      Red colors have the largest wavelengths
      (lowest frequencies), whereas blue and violet
      colors have the smallest wavelengths (highest
      frequencies)
      White light is a combination of all the colors

11,16 April 2007           PHYS 202: Chapter 24         11
             Energy Carried by Electromagnetic Waves

      In 1865, Maxwell showed                          c2 = 1/(ε0 μ0)
      and for EM waves             E=cB

      Like other waves, EM waves carry energy
             via their electric & magnetic fields


      The total energy density u of an EM wave is its
      total energy per unit volume
      In a vacuum
         u = ½ ε0 E2 + ½ B2/μ0 = ε0 E2 = B2/μ0

11,16 April 2007                PHYS 202: Chapter 24                    12
           Intensity of Electromagnetic Waves

      The intensity S of a wave is the power P it
      carries perpendicularly through a surface
      divided by the surface area A, or
                      P total energy
                    S              c u
                      A      t A




      Thus
                   S = ½ c(ε0 E2+B2/μ0) = ε0 c E2 = c B2/μ0
11,16 April 2007                 PHYS 202: Chapter 24         13
                   Example: Energy Carried by EM Waves

      On a cloudless day, the sunlight that
      reaches the earth’s surface has an
      average intensity of 1.0×103 W/m2.
      What is the average EM energy
      contained in 5.5 m3 of space just
      above the earth’s surface?



      Answer:

11,16 April 2007                 PHYS 202: Chapter 24    14
      Another Example: Energy Carried by EM Waves

      The EM wave that delivers a cell-phone call
      to a car has a magnetic field with an rms
      value of 1.5×10–10 T. The wave passes
      perpendicularly through an open window
      having an area of 0.20 m2. How much
      energy does this wave carry through the
      window during a 45-s phone call? [P24.48]


      Answer:


11,16 April 2007        PHYS 202: Chapter 24        15
          Doppler Effect for Sound

      Waves from an approaching
      source are bunched together
      Waves from a receding source
      are spread apart

      The apparent change
      in frequency of a wave
      due to the relative motion of the
      source and the observer is called
      the Doppler effect



11,16 April 2007         PHYS 202: Chapter 24   16
            Doppler Effect for Electromagnetic Waves

      When EM waves in a vacuum travel along the
      same line as the source and observer of the
      waves, the Doppler effect is given by
                                       vrel 
                           fo  fs 1        if vrel  c
                                        c 
      where
             fo is the observed frequency
             fs is the frequency emitted by the source
             vrel is the relative speed of the observer and the
             source
             the + sign applies when the observer and
             source approach each other
             the – sign applies when they move apart
11,16 April 2007               PHYS 202: Chapter 24           17
                   Example: Doppler Effect for EM Waves

      A speeder is pulling directly away and
      increasing his distance from a police car
      moving at 25 m/s relative to the ground.
      The radar gun in the police car emits an
      EM wave with a frequency of 7.0×109
      Hz. The wave reflects from the speeder’s
      car and returns to the police car, where
      the frequency is measured to be 320 Hz
      less than the emitted frequency. Find
      the speeder’s speed relative to the
      ground. [P24.48]

      Answer:

11,16 April 2007                 PHYS 202: Chapter 24     18
     Another Example: Doppler Effect for EM Waves

      The figure shows 3 situations A, B, and C in
      which an observer and a source of EM waves
      are moving along the same line. In each case,
      the source emits a wave of the same
      frequency. The arrows denote velocity vectors
      relative to the ground. Rank the frequencies of
      the observed waves in ascending order.



      Answer:



11,16 April 2007         PHYS 202: Chapter 24       19
                            Polarization
      When the vibrations of a transverse wave
      always occur along only one
      direction, the wave is said to
      be linearly polarized
             This direction is called
             direction of polarization
      A linearly polarized wave
      cannot pass through a slit
      that is perpendicular to the
      direction of polarization of
      the wave
      The idea of polarization has
      no meaning for longitudinal
      waves
11,16 April 2007                PHYS 202: Chapter 24   20
           Linearly Polarized & Unpolarized EM Waves

      In an EM wave that is linearly polarized, the
      electric field oscillates along only one
      direction, and the magnetic field also oscillates
      along only one direction which
      is perpendicular to the direction
      of the electric field
      In an unpolarized EM wave,
      such as the light from the sun
      or from an incandescent bulb,
      the direction of polarization
      does not remain fixed, but
      fluctuates randomly in time

11,16 April 2007           PHYS 202: Chapter 24        21
                     Polarizing Materials
      Linearly polarized light can be produced from
      unpolarized light with the aid of a polarizing
      material, which allows only the component of
      the electric field along one direction to pass
      through
             while absorbing the field
             component perpendicular
             to this direction
      The polarization direction
      that a polarizing material
      allows through is called
      the transmission axis
      The intensity of the transmitted polarized light
      is a half that of the incident unpolarized light
11,16 April 2007              PHYS 202: Chapter 24       22
                            Malus’ Law
      When 2 pieces of polarizing material are used
      one after the other, the 1st is called the
      polarizer and the 2nd the analyzer
      If the average intensity of the polarized light
      entering the analyzer is S0 , the average
      intensity of the light leaving the analyzer is
             S  S0 cos2θ
      θ being the angle
      between the
      transmission axes
      of the polarizer
      and analyzer
      This formula is called Malus’ law
11,16 April 2007              PHYS 202: Chapter 24      23
             Crossed Polarizer & Analyzer

An example of polarizing material is Polaroid
plastic
When Polaroid sunglasses are uncrossed, the
transmitted light is dimmed due to the extra
thickness of the tinted plastic
When the sunglasses are crossed, the
intensity of the transmitted light is reduced to
zero, corresponding to θ = 90°




Simulation
                   Example: Malus’ Law

      For each of the 3 sheets of polarizing
      material shown in the figure, the
      orientation of the transmission axis is
      labeled relative to the vertical. The incident
      beam of light is unpolarized and has an
      intensity of 1260 W/m2. Determine the
      intensity of the beam transmitted through
      the 3 sheets when θ1 = 19.0°, θ2 = 55.0°,
      and θ3 = 100.0°. [P24.36]



      Answer:


11,16 April 2007         PHYS 202: Chapter 24          25
         Polarization by Reflection

Unpolarized light incident on a surface
and reflected by it becomes partially
polarized in a direction parallel to the
surface
When worn in the usual way, Polaroid
sunglasses each have a transmission
axis oriented vertically
  They reduce glare by blocking
  horizontally polarized light


Simulation
              Questions
SAT 24.1.1

SAT 24.1.3

SAT 24.1.5

SAT 24.1.6

SAT 24.1.8

SAT 24.1.9

SAT 24.1.10

				
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