# Diffraction through a single slit by I42q7B3

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```									     Diffraction through a single slit
http://www.microscopy.fsu.edu/primer/java/diffraction/basicdiffraction/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.
http://www.math.ubc.ca/~cass/courses/m309-03a/m309-projects/krzak/
Diffraction patterns from slits of
different widths.

 Narrow gap
compared to
wavelength –
large diffraction
effect
 Condition for
minimum:
– 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).
Intensity

Source 2               Source 1

Distance
Young’s experiment
http://vsg.quasihome.com/interfer.htm

http://www.matter.org.uk/schools/Content/Interference/doubleslits_1.html
Schematic diagram of Young’s
double-slit experiment
http://qbx6.ltu.edu/s_schneider/physlets/main/doubleslitintensity.shtml

Light
source

Single
slit

http://www.walter-fendt.de/ph11e/interference.htm
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   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
Fringes
http://micro.magnet.fsu.edu/primer/java/interference/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.
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.
air
If the film is not too thick, the two
t                      Soap film
reflected beams produces an
interference effect.

http://webphysics.davidson.edu/physlet_resources/bu_semester2/c26_thinfilm.html
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
1
( n  )     Where n = 0, 1, 2, …
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
get
o


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
occurs.
 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
illuminated.
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
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://qbx6.ltu.edu/s_schneider/physlets/main/index.shtml
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,
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.

http://www.gg.caltech.edu/~zhukov/applets/film/applet.html
Thin Film of Air, Wedged-shaped (2)
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=204.0

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

Fringe Spacing, d

1       
tan             2

d


θ                      d 
t
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.
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1433.msg5413#msg5413
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
 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.
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.
http://www.matter.org.uk/schools/Content/Interference/gratings.html
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/Interference/gratingExplored.html
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
http://www.launc.tased.edu.au/online/sciences/physics/diffra/diffrac.htm

   A diffraction grating
splits a plane wave
into a number of
subsidiary waves
which can be
brought together to
form an interference
pattern.
Action of Diffraction Grating
  If d is the slit spacing then
X
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 
θ2
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
Pattern

http://micro.magnet.fsu.edu/primer/java/diffraction/diffractionorders/index.html
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.

Turntable
Collimator C                Diffraction grating

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

Hydrogen                486 nm                                 656 nm

588 nm
Neon

http://jersey.uoregon.edu/vlab/elements/Elements.html

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