### NEWTON*S RING

```NEWTON’S RINGS
INTRODUCTION
The formation of Newton’s rings is an
important application of interference of
light wave from the opposite faces of a thin
film of variable thickness.
FORMATION OF NEWTON’S
RINGS
A thin air film of increasing thickness in all
direction from one point can be easily
obtained by placing a plano-convex lens of
large radius of curvature on a plane glass
plate.
When the air film is illuminated normally by monochromatic light the
observed interference fringes are circular concentric rings with centre as the
point of contact. The rings are circular since these are the loci of points of
equal optical film thickness. The rings gradually become narrower as their radii
increase.

AB is a wave incident at point B
on plano convex lens. BD and
B1D1 are waves originating by
reflection from lower surface of
plano convex lens and upper
surface of glass plate. These two
interfere to give interference
circular fringes by reflected light.
CE and C1E1 are transmitted
waves on the other side of film.
These also produce interference
circular fringes by transmitted
light.
NEWTON’S RINGS BY REFLECTED
LIGHT
CONDITION OF MAXIMA:
2µt=(n+1/2)λ
CONDITION OF MINIMA:
2µt=nλ
RADIUS OF NEWTON’S DARK
RINGS
rn=sqrt (nλR/µ)………..(1)
BRIGHT RINGS
rn=sqrt[{(n+1/2)λR}/µ ]…….(2)
Diameter of nth ring is given by
Dn=2rn
From eqn. (1),
D1=2sqrt(λR/µ)
D2=2sqrt(2λR/µ)
D3=2sqrt(3λR/µ)
The difference in the diameters of two nearest dark rings
is given by :
D2-D1 =2sqrt(λR/µ)[sqrt2-1]=0.414*2sqrt(λR/µ)
D3 – D2 = 2sqrt(λR / µ)[sqrt3-sqrt2]=0.318*2sqrt(λR / µ)
D4 -D3 = 2sqrt(λR/µ)[sqrt4-sqrt3]=0.268* 2sqrt(λR / µ)
Hence the rings gradually becomes narrower as their radii
increases .
It can also be shown that the bright rings also gradually
become narrower as their radii increases.
NEWTONS RING BY
TRANSMITTED LIGHT
Condition of maxima:
2µt=nλ
Condition of minima:
2µt=(n+1/2)λ
Difference between newton’s rings by
reflected light and transmitted light.
In the reflected system, there is a phase change of П
between the two reflected light rays while in the
transmitted system there is a phase change of 2П
between the two transmitted light rays .
Therefore the condition of maxima and minima are
opposite in two systems.
Hence the centre in the reflected system is dark while
in the transmitted system is bright.
DETERMINATION OF WAVELENGTH BY
METHOD OF NEWTON’S RINGS
From eqn.(1), diameter of nth dark ring is
Dn=2sqrt(nλR)
Dn2=4nλR
From eqn.(1), diameter of (n+m)th dark ring is
Dn+m2 = 4 (n+m) λR
D n+m 2-Dn2= 4mλR
λ=(D n+m 2-Dn2 )/4mR ………….(3)
Hence measuring ,
n,m, Dn , Dn+m and R , λ can be determined
experimentally.
EXPERIMENTAL SET UP
The cross wire of the microscope is fixed at a particular dark
ring, say, nth and reading is noted on microscope. The
microscope is moved to diametrically opposite side and the
cross wire is fixed on the same ring and reading is noted. The
difference between the two readings will be the diameter of
that particular ring(nth) . This procedure is repeated for another
ring ,say,(n+m)th . Thus diameter of (n+m)th ring is obtained The
radius of curvature R of the lower surface of the lens is
measured by a spherometer and by putting the values in
equation (3), wavelength of light is determined.
THANKS
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