Newton Rings

1. NEWTON’S RINGS

2. 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.

3. 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.

4. 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.

5. NEWTON’S RINGS BY REFLECTED LIGHT
CONDITION OF MAXIMA:
2µt=(n+1/2)λ
CONDITION OF MINIMA:
2µt=nλ

6. RADIUS OF NEWTON’S DARK RINGS
rn=sqrt (nλR/µ)………..(1)

7. RADIUS OF NEWTON’S BRIGHT RINGS
rn=sqrt[{(n+1/2)λR}/µ ]…….(2)

8. 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.

9. NEWTONS RING BY TRANSMITTED LIGHT
Condition of maxima:
2µt=nλ
Condition of minima:
2µt=(n+1/2)λ

10. 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.

11. DETERMINATION OF WAVELENGTH BY METHOD OF NEWTON’S
RINGS
From eqn.(1), diameter of nth dark ring is
Dn=2sqrt(nλR)
Dn
2=4nλR
From eqn.(1), diameter of (n+m)th dark ring is
Dn+m
2 = 4 (n+m) λR
D n+m
2-Dn
2= 4mλR
λ=(D n+m
2-Dn
2 )/4mR ………….(3)
Hence measuring ,
n,m, Dn , Dn+m and R , λ can be determined
experimentally.

12. 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.

13. THANKS