Diffraction through a single slit by I42q7B3


									     Diffraction through a single slit

   Diffraction refers to the spreading or bending of
    waves around edges.

The fringe pattern formed by a single slit consists of
alternate bright and dark fringes and the fringes fade
away from the centre.
      Diffraction patterns from slits of
              different widths.

 Narrow gap
  compared to
  wavelength –
  large diffraction
 Condition for
    – Sin  = n/a
    – y/d  n/a
Diffraction pattern through an obstacle
Diffraction Patterns
           Resolution and Diffraction
   Resolution refers to the ability to distinguish two objects
    that are close together.
   The light from an object is diffracted by the aperture of
    the viewing instrument.
   Two neighbouring objects can be resolved provided that
    the peak from the central maximum of one is no closer
    than the first minimum of the other (and vice versa).

      Source 2               Source 1

                       Young’s experiment

          Schematic diagram of Young’s
             double-slit experiment



       Conditions for Observable
   Coherent Sources
    – Coherent sources are those which emit light
      waves of the same wavelength or frequency and
      are always in phase with each other or have a
      constant phase difference.
   Polarization
    – The wave disturbance have the same polarization.
   Amplitudes
    – The two sets of wave must have roughly equal
   Path Difference   http://www.ngsir.netfirms.com/englishhtm/Interference.htm

    – The path difference between the light waves must
      not be too great.
    Appearance of Young’s interference

 If the source slit is moved nearer to the
  double slits the separation of the fringes is
  unaffected but their brightness increases.
 If the separation of the double slits decreases,
  the separation of the fringes increases.
 If the width of slits is widened, the number of
  fringes decreases.
 If white light is used the central fringe is white
  and the fringes on either side are coloured.
Interference Fringe Pattern
          Interference by Thin Films
   Thin film interference patterns seen in
     Thin film of soapy water           Seashell

                            A thin layer of oil on the
                            Water of a street puddle
                 Parallel-sided Thin Film (1)
       Consider a film of soap with uniform thickness
        in air
                                           When a beam of light is incident
                                           on to the surface of the film, part
                                           of incident light is reflected on
                                           the top surface and part of that
                                           transmitted is reflected on the
                                           lower surface.
                                     If the film is not too thick, the two
    t                      Soap film
                                     reflected beams produces an
                                     interference effect.

     Parallel-sided Thin Film(2)
 If light travelling in a less dense medium
  is reflected by a dense medium, the
  reflected wave is phase-shifted by π.
 If light travelling in a dense medium is
  reflected by a less dense medium, the
  reflected wave does not experience any
  phase shift.
         Parallel sided Thin Film (3)
   Constructive interference occurs if the path
    difference between the two reflected light
    beams is
            ( n  )     Where n = 0, 1, 2, …
   Destructive interference occurs if the path
    difference between the two reflected light
    beams is
             n         Where n = 0, 1, 2, …
   If the film has a refractive index μ then we
     Parallel sided Thin Film (4)
 On the other hand, the part reflected at the
  lower surface must travel the extra distance of
  2 t, where t is the thickness of the film.
 That is, 2t is the path difference between the
  two reflected beams.
 If 2t = (n+½) λ then constructive interference
 If 2t = nλ then destructive interference occurs.
 When t is large, several values of λ satisfy the
  equation. The film will appear to be generally
                    Blooming of Lenses (1)

 The process of coating
  a film on the lens is
  called blooming.
 A very thin coating on
  the lens surface can
  reduce reflections of
  light considerably.

    http://mysite.verizon.net/vzeoacw1/thinfilm.html l
         Blooming of Lenses (2)
 The amount of reflection of light at a
  boundary depends on the difference in
  refractive index between the two
 Ideally, the coating material should have
  a refractive index so that the amount of
  reflection at each surface is about equal.
  Then destructive interference can occur
  nearly completely for one particular
     Blooming of Lenses (3)
 The thickness of the film is chosen so
  that light reflecting from the front and
  rear surfaces of the film destructively
 For cancellation of reflected light,
         1 o
    2t  ( )
         2 
Soap Thin Film Interference (1)
Soap Thin Film Interference (2)
  Thin Film of Air, Wedged-shaped (1)
 Light rays reflected from the upper and lower
  surfaces of a thin wedge of air interfere to
  produce bright and dark fringes.
 The fringes are equally spaced and parallel
  to the thin end of the wedge.

    Thin Film of Air, Wedged-shaped (2)

 For minimum intensity, 2t = nλ.
 For maximum intensity, 2t = (n+½)λ.

                                                   Fringe Spacing, d

                                                                       1       
                                                         tan             2


                               θ                      d 
                                                                     2 tan 
                Newton’s Rings (1)

   When a curved glass surface is placed in
    contact with a flat glass surface, a series of
    concentric rings is seen when illuminated from
    above by monochromatic light. These are
    called Newton’s rings.
          Newton’s Ring (2)

 Newton’s rings are due to interference
  between rays reflected by the top and bottom
  surfaces of the very thin air gap between the
  two pieces of glass.
 Newton’s rings represent a system of contour
  fringes with radial symmetry.
 The point of contact of the two glass surfaces
  is dark, which tells us the two rays must be
  completely out of phase.
                  Flatness of Surfaces
   Observed fringes for a wedged-shaped air film
    between two glass plates that are not flat.

   Each dark fringe
    corresponds to a region of
    equal thickness in the film.
   Between two adjacent
    fringes the change in
    thickness is λ/2μ.
        where μ is the refractive
        index of the film.
                           Multiple Slits (1)

          Double slit pattern                                   Three-slit pattern

 The fringes of the double                              There is a subsidiary
 slit pattern fade away                                 maximum between the
 from centre and                                        double slit maxima.The
 disappear at the single                                fringes become narrower
 slit minimum.                                          and sharper.
                          Multiple Slits (2)
                                                     The fringes become
                                                      sharper as the
                                                      number of slits is
                                                     The subsidiary
                                                      maxima become
                                                      less and less
                                                      significant as the
                                                      number of slits is
          Diffraction Grating
 A large number of equally spaced parallel
  slits is called a diffraction grating.
 A diffraction grating can be thought of as an
  optical component that has tiny grooves cut
  into it. The grooves are cut so small that
  their measurements approach the wave
  length of light.
              Diffraction Gratings

   A diffraction grating
    splits a plane wave
    into a number of
    subsidiary waves
    which can be
    brought together to
    form an interference
    Action of Diffraction Grating
                          If d is the slit spacing then
                           the path difference
                           between the light rays X
           θ               and Y = d sin θ.
                          For principal maxima,
     θ               Y     d sin θ = nλ.
d                         The closer the slits, the
             θ             more widely spaced are
                           the diffracted beams.
         Path difference
                          The longer the wavelength
         = d sin θ
                           of light used, the more
                           widely spaced are the
                           diffracted beams.
Number of Diffraction beams

                          Since sin θ  1,
          n=2                   n
                                  1
     θ2        n=1               d
    θ1                               d
    θ1           n=0          n 
                n=1                  
                       The highest order number
         n=2           is given by the value of d/λ
                       rounded down to the nearest
                       whole number.
Intensity of Diffraction Grating

View through Diffraction Grating

                            Spectrum of a star
   Diffraction grating    - Procyon
    placed in front of a
    methane air flame
       Using a diffraction grating to
      measure the wavelength of light
   A spectrometer is a device to measure
    wavelengths of light accurately using
    diffraction grating to separate.

             Collimator C                Diffraction grating

    Light                                θ
                                                    Telescope T
                            Achromatic                         Eyepiece
                            lenses                              Eye
                               Line Spectrum
        The appearance of the spectrum in a
         spectroscope (spectrometer)

  Hydrogen                486 nm                                 656 nm

                                                        588 nm


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