24.1)Conditions for Interference

  1. sources must be coherent; that is, they must maintain a constant phase
  with respect to each other
  
  2. Sources must have identical wavelengths
  
  3. superposition principle must apply
  
  Normal light has frequent and random phase changes.
  
 24.2)Young's double slit interference
 
  ONE light source, divided intwo two by narrows slits.  This gaurantees
  the light rays to be coherent.
  
  The resulting pattern is bright and dark parallel bands called fringes.
  
  See p. 792 figure 24.4 in book:
  
  δ = path difference =  r2 - r1 = d sin θ
  
  The condition for bright fringes or constructive interference:
  
  δ = d sin θ = m λ  
  
  where d is the distance between the slits, θ is the angle to the
  ponit on the projection screen, λ is the wavelength, and m can
  have the values 0, ±1, ±2...
  
  The condition for dark fringes or destructive interference:
  
  δ = d sin θ = (m + 1/2) λ  
  
24.3) Change of phase due to reflection 

  When light reflects it undergoes a 180 degree phase change,
  much like a wave in a tring with one staionary end.
  
24.4) Interference in thin films  
 
  The wavelength of light in a medium with index of refraction n is
  
  λn = λ/n
  
  where λ is the wavelength of light in a vacuum.
  
  
  Condition for constructive interference:
  
  2t = (m + 1/2)λn
  
  where t is the thickness of the material, m is 0,1,2...
  
  Note: in the above equation λn is the wavelength of light
  in the material.
  
  Condition for destructive interference:
  
  2nt = (m + 1/2)λ  
  
  Note: in the above equation, &lambda is the wavlength of light in a vacuum.
  
  
  This causes the phenomenon known as Newton's rings.
  
  
24.5) Diffraction  

  Diffraction occurs when light passes through a small slit
  that is about the magnitude of the wavelength of the light.
  
  see Figure 24.11 and 24.12 on p. 801
  
  
24.6) Single Slit Diffraction 

  the general condition for destructive interference with a single is
  
  sin θ = m (λ/a)
  
  Where a is the width of the slit.
  
24.7) Polarization of light 

  Polarized light has an electric field vector and a magnetic field vector which
  are perpendicular to each other.  This is firm evidence of the 
  transverse nature of electromagnetic waves.
  
  In normal light the electric field vector and magnetic field vector can 
  oscillate in any direction.
  
  
  Polarization by selective absorption:
  
  certain materials, called polaroids, transmit light waves whose electric
  fields are parallel to a certain diretion and absorbs those that are
  perpendicular to that direction.
  
  two polarizing in materials used in conjunction:
  
  I = I0 cos2 θ
  
  Where I 0 is the intensity of the incident light, I is the 
  intensity of the transmitted light, and θ is the angle in between the
  polarizer and the analyzer.
  
  
  Polarization by Reflection:
  
  for angles between 0 and 90, the reflected light is polarized to some extent.
  At a particular angle, the reflected light is completely polarized.  That
  angle depends on the index of refraction for the material.
  
  n = tan θp
  
  Where n is the index of refraction and θ is the polarizing angle.
  
  
  Polarization by scattering:
  
    sunlight is polarized by air molecules.  Bees and homing pigeons use this
	as navigation.
	
	
 Optical Activity:
 
   A material that rotates the angle of polarization is said to be
   optically active.
   
 Application: Liquid Crystals
 
 LCD - Liquid Crystal Display
 
 Uses the concept of optical activity.  An LCD element uses two polarizers and a
 crystal in between.  The crystal is optically active only when voltage
 is applied to it, thereby allowing no light to pass through and creating a
 black section.
 An LCD element  is optically inactive when no voltage is applied to it, 
 allowing light to pass through.

 

  
HW 9:
p. 814  # 1   
p. 815 #14 
p. 816 #27, 33