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
– Sin = n/a
– y/d n/a
Diffraction pattern through an obstacle
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
Schematic diagram of Young’s
Conditions for Observable
– 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.
– The wave disturbance have the same polarization.
– 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
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
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
If the film is not too thick, the two
t Soap film
reflected beams produces an
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
Parallel sided Thin Film (3)
Constructive interference occurs if the path
difference between the two reflected light
( n ) Where n = 0, 1, 2, …
Destructive interference occurs if the path
difference between the two reflected light
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
A very thin coating on
the lens surface can
reduce reflections of
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,
2t ( )
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
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
less and less
significant as the
number of slits is
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.
A diffraction grating
splits a plane wave
into a number of
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.
The longer the wavelength
= d sin θ
of light used, the more
widely spaced are the
Number of Diffraction beams
Since sin θ 1,
θ2 n=1 d
θ1 n=0 n
The highest order number
n=2 is given by the value of d/λ
rounded down to the nearest
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
The appearance of the spectrum in a
Hydrogen 486 nm 656 nm