Diffraction through a single slit

1
Diffraction through a single slit
http//physicsstudio.indstate.edu/java/physlets/ja
va/slitdiffr/index.html

• 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.
2
Diffraction pattern through an obstacle
3
Diffraction Patterns
4
Youngs experiment
http//www.matter.org.uk/schools/Content/Interfere
nce/doubleslits_1.html
5
Schematic diagram of Youngs double-slit
experiment
http//www.walter-fendt.de/ph11e/interference.htm
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Conditions for Observable Interference

• 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
  amplitude.
• Path Difference
• The path difference between the light waves must
  not be too great.

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Appearance of Youngs interference Fringes
http//micro.magnet.fsu.edu/primer/java/doubleslit
/index.html

• 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.

8
Interference Fringe Pattern
9
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
10
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.
air
If the film is not too thick, the two reflected
beams produces an interference effect.
Soap film
http//webphysics.davidson.edu/physlet_resources/b
u_semester2/c26_thinfilm.html
11
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 p.
• If light travelling in a dense medium is
  reflected by a less dense medium, the reflected
  wave does not experience any phase shift.

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Parallel sided Thin Film (3)

• Constructive interference occurs if the path
  difference between the two reflected light beams
  is

Where n 0, 1, 2,

• Destructive interference occurs if the path
  difference between the two reflected light beams
  is

Where n 0, 1, 2,

• If the film has a refractive index µ then we get

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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 (n½) ? then constructive interference
  occurs.
• If 2t n? then destructive interference occurs.
• When t is large, several values of ? satisfy the
  equation. The film will appear to be generally
  illuminated.

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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//users.erols.com/renau/thinfilm.html
15
Blooming of Lenses (2)

• The amount of reflection of light at a boundary
  depends on the difference in refractive index
  between the two materials.
• 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 wavelength.

http//www3.ltu.edu/s_schneider/physlets/main/thi
nfilm.shtml
16
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 interferes.
• For cancellation of reflected light,

17
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.

http//www.gg.caltech.edu/zhukov/applets/film/app
let.html
18
Thin Film of Air, Wedged-shaped (2)

• For minimum intensity, 2t n?.
• For maximum intensity, 2t (n½)?.

Fringe Spacing, y
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Newtons 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 Newtons
  rings.

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Newtons Ring (2)

• Newtons 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.
• Newtons 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.

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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 ?/2µ.
• where µ is the refractive index of the film.

22
Multiple Slits (1)
Three-slit pattern
Double slit pattern
The fringes of the double slit pattern fade away
from centre and disappear at the single slit
minimum.
There is a subsidiary maximum between the double
slit maxima.The fringes become narrower and
sharper.
http//www.matter.org.uk/schools/Content/Interfere
nce/gratings.html
23
Multiple Slits (2)

• The fringes become sharper as the number of slits
  is increased.
• The subsidiary maxima become less and less
  significant as the number of slits is increased.

http//www.matter.org.uk/schools/Content/Interfere
nce/gratingExplored.html
24
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.

25
Diffraction Gratings

• A diffraction grating splits a plane wave into a
  number of subsidiary waves which can be brought
  together to form an interference pattern.

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Action of Diffraction Grating

• If d is the slit spacing then the path difference
  between the light rays X and Y d sin ?.
• For principal maxima,
• d sin ? n?.
• The closer the slits, the more widely spaced are
  the diffracted beams.
• The longer the wavelength of light used, the more
  widely spaced are the diffracted beams.

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Number of Diffraction beams

• Since sin ? ? 1,

• The highest order number is given by the value of
  d/? rounded down to the nearest whole number.

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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.

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View through Diffraction Grating

• Spectrum of a star
• - Procyon

• Diffraction grating placed in front of a methane
  air flame