Newton

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Newtons Rings
2
A
B
Plano convex lens
Air film
Q
P
O
Glass plate
Thickness of air film is zero at point of contact
O.
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Reflected light
L
Air film
G
Circular interference fringes are formed by
reflected light
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Microscope
45º
S
glass
L
Lens
Air film
Glass plate
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Interference occurs between the light reflected
from the lower surface of the lens and the
upper surface of the glass plate G.
Since the convex side of the lens is a spherical
surface, the thickness of the air film will
be cons- tant over a circle (whose centre will be
at O ) and we will obtain concentric dark and
bright rings.
Newtons rings
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It should be pointed out that in order to observe
the fringes the microscope has to be focused on
the Surface of the film.


Each ring will be locus of all such points where
thickness is same.


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Condition for bright ring will be
For air film , ? 1 and for near normal
incidence r is very small and hence cos r 1
Thus,
Where n 0,1,2,3.
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For dark rings,
Again for air film ? 1 and for small r we
have Condition for dark rings,
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O
R
R - tn
A
B
tn
tn
M
N
rn
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R radius of curvature of lens t thickness of
air film at a distance AB rn OA R - t

• From ?OAB
• R2 (R t)2rn2
• rn2 R2 - (R t)2 R2 - R2 t2 2Rt 2Rt t2
• As Rgtgtt , rn2 2Rt
• ? t rn2/2R

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So condition for bright rings 2t
(2n1)?/2
n 0,1,2,3,.
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Similarly for dark rings,
n 0,1,2,3,.
Diameter of dark rings,
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CENTER IS DARK
At n 0, radius of dark ring 0.
radius of bright ring
Alternately dark and bright rings will be
produced.
The spacing between second and third dark
rings is smaller than the spacing between the
first and second one.
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Consider the diameter of dark rings
Four fringes
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Fringe width decreases with the order of
the Fringe and fringes get closer with increase
in their order.
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Wavelength determination
Radius of the nth dark ring rn is given by
Similarly for (nm)th dark band
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(2) (1)
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Suppose diameter of 6th and 16th ring
are Determined then, m 16-6 10
So
Radius of curvature can be accurately
measured with the help of a spherometer and
therefore by measuring the diameter of dark or
bright ring you can experimentally determine the
wavelength.
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Newtons rings with transmitted light
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Transmitted light
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Condition for bright fringes
Condition for dark fringes
For air as thin film and near normal incidence
? 1 and cosr 1
So for bright fringes, 2t n?
For dark fringes,
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But we know that
, r radius of ring
For bright rings
For dark rings
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If we put n 0 then r 0 for the bright ring
So for Newton's rings for transmitted rays the
central ring will be bright.
CENTRAL RING IS BRIGHT.
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WAVELENGTH DETERMINATION
We know radius of the nth dark ring rn is
.(1)
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Similarly,
..(2)
(2) (1)
..(3)
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Suppose diameter of the 8th and 18th ring
are Determined then, m 18-8 10 and
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Refractive index determination
air
Diameter of the dark rings
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?
Liquid of refractive index ?
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(for near normal incidence and ?glt?
Condition for dark ring formation
..(4)
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Similarly we can get
.(5)
(5) (4)
So,
.(6)
This is the value of ? if ? is known.
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? Can also be determine if ? is unknown
We have from equation (3) and (6)
..(3)
.(6)
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Divide (3)/(6)