NEWTON’S RINGS EXPERIMENT

AIM: To determine the wavelength of sodium light using newton’s rings

Newton's rings is a phenomenon in which an interference pattern is created by

the reflection of light between two surfaces—a spherical surface and an adjacent touching flat
surface. When viewed with monochromatic light, Newton's rings appear as a series of concentric,
alternating bright and dark rings centered at the point of contact between the two surfaces. When
viewed with white light, it forms a concentric ring pattern of rainbow colors, because the
different wavelengths of light interfere at different thicknesses of the air layer between the
surfaces. Probably the first measurement of the wavelength of light was made by Newton (Isaac
Newton, who first studied the effect in 1717).

Beam Splitter

FIGURE 1

The pattern is created by placing a very slightly curved glass (lens) on a flat glass plate. The two
pieces of glass make contact only at the center, at other points there is a slight air gap between
the two surfaces, increasing with radial distance from the center.
The above diagram (Fig. 1) shows a small section of two pieces, with the gap increases as we
move away from the centre. Light from a monochromatic source shines through the top piece
and reflects from both the bottom surface of the top piece and the top surface of the optically flat
glass surface, and the two reflected rays combine and superpose.
However the ray reflecting off the bottom surface travels a longer path. The additional path
length is equal to twice the gap between the surfaces. In addition the ray reflecting off the bottom
piece of glass undergoes a 180° phase reversal, while the internal reflection of the other ray from
the underside of the top glass causes no phase reversal.

Constructive interference (a): In areas where the path length difference between the two rays is
equal to an even multiple of wavelength (λ) of the light waves, the reflected waves will be in
phase. Therefore, the waves will reinforce (add) and the resulting reflected light intensity will be
greater. As a result, a bright area will be observed there.
Destructive interference (b): At other locations, where the path length difference is equal to an
odd multiple of wavelength, the reflected waves will be 180° out of phase, As a result, a dark
area will be observed there. Because of the 180° phase reversal due to reflection of the bottom
ray, the center where the two pieces touch is dark.

The path difference between the two rays one reflected from top and bottom surfaces (with
thickness of the film t) is

2µ t cosθ; where θ is the angle of refraction in the air film and for an air film (µ = 1) between
the lens and the glass plate. Then the path difference is: 2 t cosθ

The ray reflected from bottom suffers an additional phase change of π or a further increase in
the path difference by λ/2 . Hence the total path difference between the two rays is
2 t cosθ + λ/2; Since the rays are incident normally, θ is zero and hence Cos(θ) =1 .

Condition for dark ring (destructive interference)

2 t + λ/2 = (m + 1/2) λ ; => t = m λ/2 (1)

Consider condition for formation of dark fringes due to interference of reflected beams in a film
of thickness ‘t’ and refractive index ‘µ’. According to geometrical theorem, the product of
intercepts of intersecting chord is equal to the product of sections of diameter then,

R2 = rm2 + (R-tm)2 ; where R = radius of curvature of the lens, could be calculated as

cm
l = distance between two legs of spherometer
h = height of the plano-convex lens

Hence, R = [rm2 + tm2] / 2 tm ; for small thickness (tm << 1)

=> rm2 = 2 R tm (2)

Using any of the two relations, we can find the wavelength of the monochromatic light used.

rm2= 2 R (m λ/2) = R m λ
Thus if Dn and Dn+m denotes the diameters of nth and (n+m)th dark fringes then we have ,
Subtracting we get the required wavelength of the source

Procedure:
1. Click on the "light on" button.
2. Select the lens of desirable radius of curvature.
3. Adjust the microscope position to view the Newton’s rings.
4. Focus the microscope to view the rings clearly.
5. Fix the cross-wire on say 20th ring either from right or left of the centre dark ring and take
the readings.
6. Move the crosswire and take the reading of 18th, 16th...........2nd ring.
7. You have to take the reading of rings on either side of the centre dark ring.
8. Enter the readings in the tabular column.
9. Calculate the wavelength of the source by using the given formula.

Observations:

To find Least Count

One main scale division = ............... cm

Number of divisions on Vernier = ...............

L.C = One main scale division/ Number of division on Vernier =.................................

Calculation:

Mean value of, D2m+n - D2n = .......cm2

Wavelength of light λ = (D2m+n - D2n) / 4 m R

=.............................nm

Result:

Wavelength of light from the given source is found to be = ..........nm