engphyunit 3-interference 3
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A plano-convex lens of large radius of curvature R is placed on
a plane glass plate with its curved surface downwards and is
illuminated from above with a parallel beam of monochromatic
light. Some of the light is reflected from the upper surface of the
glass plate and some from the lower surface of the lens;
interference thus occurs by division of amplitude, the fringes
being localised in the air gap between the lens and plate.
Ray 1 undergoes a phase change of 180 on
reflection, whereas ray 2 undergoes no phase
change
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Experimental arrangementR= radius of curvature of lens
r=radius of Newton’s ring
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JITENDRA PAL SINGH
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Newton's rings in a thin film of diesel oil
on a wet road, seen in white light
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...2
11
,,
)()(
,
,
2
22
22
R
rRR
rRRt
rQMRCQtMO
QMCQMO
CMQIn
RCO
MOCOt
Radius of Newton,s Ring
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9
2
22
1.2
2
1
.2
1
,2
11
2
2
2
2
2
2
R
r
R
rdifferencePath
R
rt
R
rRRRt
RrastermsorderhighergNegelectinR
rRRt
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JITENDRA PAL SINGH
Radius of Bright Fringe
2
)12(
2)12(
2)12(
22)2(
2)2(
2
2
2
2
Rnr
Rnr
Rnr
nR
r
nR
r
Path difference should be an even multiple of λ/2.
i. e.
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Diameter of the bright
fringes,
.........3,2,1,)12(
tan2
2.)12(2).12(
2
)12(22
nnD
tconsR
RnRnD
RnrD
n
n
Thus the diameter of bright fringes are proportional to the
square-root of the odd natural numbers.
Ratio of Diameter
for few rings , 646.2:236.2:732.1:1:::
7:5:3:1:::
4321
4321
DDDD
DDDD
Separation between successive rings = 0.732:0.504:0.410
Thus seperation between consecutive bright rings decreases as
the order increases.
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JITENDRA PAL SINGH
Radius of Dark Fringe
....3,2,1,0,
.2
.2
.2
.22
)112(
22)12(
2)12(
2
2
2
2
nRnr
Rnr
RnRnr
nR
r
nR
r
Path difference should be an odd multiple of λ/2.
i. e.
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Diameter of the dark fringes,
.........3,2,1,0,
tan4
2..4
22
nnD
tconsR
RnRnD
RnrD
n
n
Thus the diameter of bright fringes are proportional to the
square-root of natural numbers.
Ratio of Diameter
for few rings , 2:732.1:414.1:1:0:::
4:3:2:1:0:::
4321
4321
DDDD
DDDD
Separation between successive rings = 1:0.414:0.318:0.268
Thus separation between consecutive dark rings also decreases
as the order increases.
Thus, central ringes are broader and peripheral rings are closer.
NEWTON’S RINGS
Ray 1 undergoes a phase change of 180 on
reflection, whereas ray 2 undergoes no phase
change
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An antireflective or anti-reflection (AR) coating is a type
of optical coating applied to the surface of lenses and other optical
devices to reduce reflection.
This improves the efficiency of the system since less light is lost.
In complex systems such as a telescope, the reduction in
reflections also improves the contrast of the image by elimination
of stray light.
This is especially important in planetary astronomy. In other
applications, the primary benefit is the elimination of the reflection
itself, such as a coating on eyeglass lenses that makes the eyes
of the wearer more visible to others, or a coating to reduce the
glint from a covert viewer's binoculars or telescopic sight.
Definition11/20/2012
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Many coatings consist of transparent thin film structures with
alternating layers of contrasting refractive index.
Layer thicknesses are chosen to produce destructive
interference in the beams reflected from the interfaces, and
constructive interference in the corresponding transmitted
beams.
This makes the structure's performance change with
wavelength and incident angle, so that color effects often
appear at oblique angles.
A wavelength range must be specified when designing or
ordering such coatings, but good performance can often be
achieved for a relatively wide range of frequencies: usually a
choice of IR, visible, or UV is offered.
Principle11/20/2012
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Figure shows the phenomena of interference that lead to
antireflecting coating. In this the refractive index of the coating
material is choosen that it has an intermediate value between
the glass and air.
For example that refractive index of MgF2 is 1.38.
The ray AB is incident on the system and at point B it suffers
reflection on the surface of AR coating (denser medium) and
proceeds along BC. A part of it moves along BD in the same
medium and at D it suffers reflection again at the surface of
denser (glass) and emerges out of along EF in air.
Hence, same phase change occurs in both the rays at
reflection.
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JITENDRA PAL SINGH
AIR μair=1.0
AR Coating, MgF2, μF=1.38
Glass, μglass=1.5
A
B
C
D
E
F
i
r
r
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rt
rt
rt
cos2
cos2
22cos2
Reflection at glass/AR coating and AR coating/air bounaries
will produce phase change of π.
Path difference = 2
.2
Total path difference
Term ‘λ’ may be omitted as addition and subtraction of λ
will not affect the path difference.
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For normal incidence,
Path difference = 2μ.t
Where, μ and t are refractive index and thickness of AR
coating material respectively.
For condition of destructive interference, 2μ.t= (2n+1).(λ/2)
where, n=0,1,2..
For n=0
2μ.tmin = λ/2
tmin= λ/4 μ
Minimum thickness of the coating required for no reflection at
the centre of visible spectrum (λ = 5.5×10-5 cm)
cmt
cmt
5
min
5
min
10966.0
38.14
105.5
4
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JITENDRA PAL SINGH
If the refractive of thin films coated on glass is higher than that
of glass, then reflectivity of glass surface is increased and the
coating is known as high reflection coating.
Path difference in this case will be given by
For normal incidence2
cos2
rt
22
t
For constructive interference, 2μ.t - (λ/2) =nλ, where, n=0,1,2..
2μ.t = (2n+1)λ/2
For n=0, 2μ.tmin = λ/2
tmin= λ/4 μ
Minimum thickness of the coating required for no reflection at
the centre of visible spectrum (λ = 5.5×10-5 cm)
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An intereference filter is a optical system that
transmits a very narrow range of wavelength and
provides a monochromatic beam of light.
They are composed of transparent glass or
quartz substrate on which multiple thin layers of
dielectric material, sometimes separated by
spacer layers
Permit great selectivity
Definition11/20/2012
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JITENDRA PAL SINGH
CONSTRUCTION OF FILTERS
Filter
components
Single Optical
filter
“optical
glue” or
mostly filters
are spatter
Coated in a
vacuum
Interference
Filters
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TRANSMISSION DETERMINATION
Constructive and destructive interference
occurs between reflections from various
layers
Transmission determined by :
thickness of the dielectric layers
number of these layers
angle of incident light on the filters
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INTERFERENCE FILTERS ADVANTAGES
They can be used as reflectors in two and
three color analysis.
They usually do not themselves produce
fluorescence.
They are available in short pass versions.
They are excellent as primary barrier filters.
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JITENDRA PAL SINGH
INTERFERENCE FILTERS: DISADVANTAGES
Have lower blocking properties
Reduced passing properties
Their reflecting and passing properties
are not absolute, this should be
considered while dealing with multiple
wavelengths
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