Chapter 27- Phys

• Wave Optics


  The wave nature of light is needed to explain various phenomena
• Interference


  Light waves interfere with each other much like mechanical waves do
• Diffraction


  The spreading out of light from its initial line of travel when waves pass through small openings, around obstacles or by sharp edges
• Polarization


  The particle nature of light was the basis for ray (geometric) optics
• Interference


  All interference associated with light waves arises when the electromagnetic fields that constitute the individual waves combine
• Conditions for Interference


  • The sources are coherent
  • The waves have identical wavelengths
• Young's Double Slit Experiment


  1. Light is incident on a screen with a narrow slit, So

  2. The light waves emerging from this slit arrive at a second screen that contains two narrow, parallel slits, S1 and S2
• Young's Double Slit Experiment


  • The narrow slits, S1 and S2 act as sources of waves
  • The waves emerging from the slits originate from the same wave front and therefore are always in phase
• Resulting Interference Pattern


  • The light from the two slits form a visible pattern on a screen
  • The pattern consists of a series of bright and dark parallel bands called fringes
  • Constructive interference occurs where a bright fringe appears
  • Destructive interference results in a dark fringe
• Interference Patterns


  • Constructive interference occurs at the center point
  • The two waves travel the same distance, therefore they arrive in phase
  • The upper wave has to travel farther than the lower wave, the upper wave travels one wavelength farther, therefore the waves arrive in phase, a bright fringe occurs
  • The upper wave travels one-half of a wavelength farther than the lower wave, the trough of the bottom wave overlaps the crest of the upper wave, this is destructive interference, a dark fringe occurs
• Interference Equations


  The path difference, δ, is found from the small triangle

  δ = r2 – r1 = d sin θ

  This assumes the paths are parallel
• Interference Equations for Bright Fringes


  For a bright fringe, produced by constructive interference, the path difference must be either zero or some integral multiple of the wavelength

  δ = d sin θbright = m λ

  m = 0, ±1, ±2, …

  m is called the order number

  When m = 0, it is the zeroth order maximum

  When m = ±1, it is called the first order maximum
• Interference Equations for Dark Fringes

  When destructive interference occurs, a dark fringe is observed

  This needs a path difference of an odd half wavelength

  δ = d sin θdark = (m + ½) λ

  m = 0, ±1, ±2, …
• Interference Equations for Fringe Positions


  The positions of the fringes can be measured vertically from the zeroth order maximum

  y = L tan θ ≈ L sin θ

  Assumptions: L >> d, d >> λ

  Approximation: θ is small and therefore the approximation tan θ ≈ sin θ can be used
• The approximation is true to three-digit precision only for angles less than about 4°
• Interference Equations


  • For bright fringes

  For dark fringes
• Uses for Young's Double Slit Experiment


  • Young's Double Slit Experiment provides a method for measuring wavelength of the light

  This experiment gave the wave model of light a great deal of credibility

  It is inconceivable that particles of light could cancel each other
• Change of Phase Due to Reflection


  The positions of the dark and bright fringes are reversed relative to pattern of two real sources

  This is because there is a 180° phase change produced by the reflection
• Phase Changes Due To Reflection


  There is no phase change when the wave is reflected from a boundary leading to a medium of lower index of refraction
• Interference in Thin Films


  Interference effects are commonly observed in thin films

  The interference is due to the interaction of the waves reflected from both surfaces of the film
• Facts to remember about Interference in Thin Films


  • An electromagnetic wave traveling from a medium of index of refraction n1 toward a medium of index of refraction n2 undergoes a 180° phase change on reflection when n2 > n1

  There is no phase change in the reflected wave if n2 < n1

  The wavelength of light λn in a medium with index of refraction n is λn = λ/n where λ is the wavelength of light in vacuum
• Interference in Thin Films


  • Ray 1 undergoes a phase change of 180° with respect to the incident ray

  Ray 2, which is reflected from the lower surface, undergoes no phase change with respect to the incident wave

  Ray 2 also travels an additional distance of 2t before the waves recombine
• Conditions for Constructive and Destructive Interference in Thin Films


  For constructive interference: 2 n t = (m + ½ ) λ, m = 0, 1, 2 ...

  For destructive interference: 2 n t = m λ, m = 0, 1, 2 ...
• Interference in Thin Films


  Two factors influence interference: possible phase reversals on reflection and differences in travel distance

  The conditions are valid if the medium above the top surface is the same as the medium below the bottom surface

  If the thin film is between two different media, one of lower index than the film and one of higher index, the conditions for constructive and destructive interference are reversed
• Be sure to include two effects when analyzing the interference pattern from a thin film: path length and phase change
• Newton's Rings


  Another method for viewing interference is to place a planoconvex lens on top of a flat glass surface

  The air film between the glass surfaces varies in thickness from zero at the point of contact to some thickness t

  A pattern of light and dark rings is observed, called Newton's Rings

  The particle model of light could not explain the origin of the rings

  Newton's Rings can be used to test optical lenses
• Problem Solving Strategy with Thin Films


  Identify the thin film causing the interference

  Determine the indices of refraction in the film and the media on either side of it

  Determine the number of phase reversals: zero, one or two

  The interference is constructive if the path difference is an integral multiple of λ and destructive if the path difference is an odd half multiple of λ

  The conditions are reversed if one of the waves undergoes a phase change on reflection

  Substitute values in the appropriate equation, solve and check
• Equations for Thin Film Interference


  • 2nt = (m + 1/2)λ, constructive interference with 1 phase reversal

  2nt = mλ, destructive interference with 0 or 2 phase reversals
• Interference in Thin Films, Example


  • An example of different indices of refraction: a coating on a solar cell

  There are two phase changes
• CD's and DVD's


  Data is stored digitally as a series of ones and zeros read by laser light reflected from the disk

  Strong reflections correspond to constructive interference, these are chosen to represent zeros

  Weak reflections correspond to destructive interference, these are chosen to represent ones
• CD's and Thin Film Interference


  A CD has multiple tracks consisting of a sequence of pits of varying length formed in a reflecting information layer

  The pits appear as bumps to the laser beam

  The laser beam shines on the metallic layer through a clear plastic coating
• Reading a CD


  As the disk rotates, the laser reflects off the sequence of bumps and lower areas into a photodetector

  The photodetector converts the fluctuating reflected light intensity into an electrical string of zeros and ones

  The pit depth is made equal to one-quarter of the wavelength of the light

  When the laser beam hits a rising or falling bump edge, part of the beam reflects from the top of the bump and part from the lower adjacent area, this ensures destructive interference and very low intensity when the reflected beams combine at the detector

  The bump edges are read as ones, the flat bump tops and intervening flat plains are read as zeros
• DVD's


  DVD's use shorter wavelength lasers

  The track separation, pit depth and minimum pit length are all smaller

  Therefore, the DVD can store about 30 times more information than a CD
• Diffraction


  Huygen's principle requires that the waves spread out after they pass through slits

  This spreading out of light from its initial line of travel is called diffraction

  In general, diffraction occurs when waves pass through small openings, around obstacles or by sharp edges
• Single Slit Diffraction Pattern


  A single slit placed between a distant light source and a screen produces a diffraction pattern

  It will have a broad, intense central band

  The central band will be flanked by a series of narrower, less intense secondary bands (called secondary maxima)

  The central band will also be flanked by a series of dark bands (called minima)
• The results of the single slit cannot be explained by geometric optics
• Fraunhofer Diffraction


  Fraunhofer Diffraction occurs when the rays leave the
• Pit depth of a CD

  • 24.5
• Diffraction


  Huygen's principle requires that the waves spread out after they pass through slits. This spreading out of light from its initial line of travel is called diffraction. In general, diffraction occurs when waves pass through small openings, around obstacles or by sharp edges.
• Diffraction, 2


  A single slit placed between a distant light source and a screen produces a diffraction pattern. It will have a broad, intense central band. The central band will be flanked by a series of narrower, less intense secondary bands. Called secondary maxima. The central band will also be flanked by a series of dark bands. Called minima.