Interference due to transmitted light in

1
Interference due to transmitted light in
thin films
2
P
s
P
S
r
r
AIR
i
i
C
AIR
C
C
A
A
r
r
?
t
?
t
r
r
M
r
r
M
B
D
r
B
D
i
r
i
i
AIR
AIR
N
i
N
Q
Q
R
R
3
Here at B reflection takes place at the
rarer Medium .so no phase change change
occurs. BM normal to CD and DN normal to BR.
So optical path difference between DQ and BR is
x ?(BCCD) -BN
4

• n1sini n2sinr
• Sinr sini
• sini/sinr

In ?BND, siniBN/BD In ?BMD,
sinrMD/BD

• sini/sinr BN/MD

?BN ?MD
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Since ltCPBltCBPr and BCCPCD
x ?(BCCD) BN ?(DP)- ?(MD) ?(DP-MD)
?(MP)
In ?BPM cosr MP/BP So MP BP cosr
2t cos r since BP2t
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SO, x ? PM 2 ?t cos r
Conditions for constructive interference will be
2 ?t cos r n?
And conditions for destructive interference will
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One of the important applications of the thin
film interference is reducing the reflectivity of
lens surface.
n1
ai
ar
n1gt n2
at
n2
8
ai, ar, at are amplitudes of incident,reflected
and transmitted waves.
n2gtn1 , ar is negative showing that reflection
occurs at a denser medium a phase change ? comes
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r and t are reflection and transmission coefficien
ts
10
ra
a
n2
n1
ta
11
These are the Stokes relations.
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Non reflecting films

• Reflectivity is the fraction of incident light
  reflected by a surface for normal incidence.
• Reflectivity depends upon the refractive index ?
  of the material. It is given by
• For glass ? 1.5.
• Reflectivity 0.04
• 4 of incident light is reflected for normal
  incidence. Remaining 96 is transmitted.

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• The loss of energy due to reflection is one major
  reason of clarity reduction. There is also a
  reduction in the intensity of the images since
  less light is transmitted through the lenses.
• When films are coated on lens of prism surface
  the reflectivity of these surfaces is appreciably
  reduced.
• Initially the coating were made by depositing
  several monomolecular layers of an organic
  substance on glass plates.
• Now it is done by either evaporating calcium or
  magnesium fluoride on the surface in vacuum or by
  chemical treatment of the surface with acids
  which leave a thin layer of silica on the
  surface.
• No light is destroyed by non reflecting film, but
  there is redistribution means decrease in
  reflection results increase in transmission.

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Thickness of nonreflecting thin film
1
2
r
a
air(?a)
film(?f)
t
glass(?g)
?g? ?fgt ?a
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Two interfering beams will interfere
constuctively if
2?ftcosr n?
Rays will interfere destructively if
2?ftcosr (2n1)?/2
For normal incidence ltr900
2?ft (2n1)?/2
So 2?ft ?/2 for min thickness, n 0
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If a film having thickness of ?/4?f and having
refractive index less than that of the glass is
coated on glass, then waves reflected from the
upper surface of the film destructively interfere
with the waves reflected from the lower surface
of the film. Such a film known as a non
reflecting film.
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ar
1
2
artt
a
r, t
na
nf
r, t
art
at
ng
Amplitude of ray 1 ar Amplitude of ray 2
artt
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For complete destructive interference ray 1 and 2
must Have the same amplitude, i.e.
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This equation gives the estimate of refractive
index of This film which should be coated on a
surface to reduce Its reflectivity. If na 1 (for
air) and ng refractive index of glass then