Newton

1
Newtons rings between two curved surfaces
2
B
A
R2
C
D
R1
P
Air film
Q
L
0
x
t be the thickness of air film at point P is PQ.
t PQ PL - QL
3
PL x2/2R1 AND QL
x2/2R2
4
The effective path difference between the two
interfering Rays in reflected light, for normal
incidence is in case of Bright rings
n 0,1,2,3..
5
Assume that the nth bright ring passes through
the point P. If rn is the radius of nth bright
ring, then x rn
6
If Dn be the diameter of nth bright ring then
7
For dark ring of reflected light
similarly
Assume that the nth dark ring passes through the
point P. If rn is the radius of nth bright ring,
then x rn
8
If Dn be the diameter of nth dark ring then
9
P
R1
o
L
x
R2
Q
10
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11
For nth bright ring
12
For nth dark ring
13
T
S
Q
P
N
i
i
AIR
U
A
C
U
i
O
r
M
t
?
r
r
r
E
L
B
L
AIR
r
P
14
Here interference pattern will not be
perfect Because intensities AT and CQ will not be
the same And their amplitude are different.
Amplitude depends on amount of light reflected
and transmitted through the films.
Intensity never vanishes completely and
perfectly dark fringes will not be observed.
But for multiple reflection intensity of minima
will be zero.
15
5
4
1
2
3
ar1
atrt
atr7t
atr5t
atr3t
a
rarer
atr3
atr7
atr5
atr
denser
at
atr2
atr4
atr6
atr8
atr4t
atr2t
atr6t
att
rarer
16
Amplitude of incident ray a Reflection
coefficient r1 and r Transmission coefficient
from rarer to denser medium t Transmission
coefficient from denser to rarer medium t
The amplitudes of the reflected rays are ar,
atrt, atr3t, atr5t, atr7t
17
When ray 1 is reflected from the surface of
denser medium it undergoes a phase change ?
Rays 2, 3, 4 are all in phase but out of phase
with ray 1 by ?
Resultant amplitude of 2, 3, 4, 5 .. is
A atrtatr3tatr5tatr7t..
attr1r2r4r6 attr
18
According to the principle of reversibility
tt 1- r12 and r - r1
So the resultant amplitude of 2,3,4, is equal
in Magnitude of the amplitude of ray 1 but out of
Phase with it.
19
One of the important applications of the thin
film interference is reducing the reflectivity of
lens surface.
n1
ai
ar
n1gt n2
at
n2
20
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
21
r and t are reflection and transmission coefficien
ts
22
ra
a
n2
n1
ta
23
These are the Stokes relations.
24
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.

25

• 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.

26
Thickness of nonreflecting thin film
1
2
r
a
air(?a)
film(?f)
t
glass(?g)
?g? ?fgt ?a
27
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
28
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.
29
ar
1
2
artt
a
r, t
na
nf
r, t
art
at
ng
Amplitude of ray 1 ar Amplitude of ray 2
artt
30
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31
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32
For complete destructive interference ray 1 and 2
must Have the same amplitude, i.e.
33
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34
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
35

• A soap film of refractive index ? is illuminated
  with white light incident at an angle i. the
  light refracted by it is examined and two bright
  bands focused corresponding to wave lengths ?1
  and ?2. show that the thickness of the film is

• White light falls normally upon a film of soapy
  water whose thickness is 5 x 10-5 cm and
  refractive index is 1.33. what wavelength in the
  Visible region will be reflected more strongly?