NEWTON’S RINGS SET UP

Engineering Physics Lab Manual

National Institute of Technology, Sikkim

1 Aim
Determination of the radius of curvature of the Plano-convex lens by using Newton’s rings apparatus

2 Apparatus Required:
• A nearly monochromatic source of light (source of sodium light)
• A plano-convex lens

• An optically flat glass plate

• A convex lens
• A traveling microscope

3 Description of the Apparatus

The experimental setup for Newton’s ring is shown in the figure 1. The convex surface of a plano-
convex lens having a long focal length (large radius of curvature) is placed in contact with a plane
glass plate and clamped together. Light from a monochromatic source (e.g., sodium lamp) is allowed
to fall on a convex lens through a wide slit, which renders it into a nearly parallel beam. At first,
light falls on a glass plate inclined at an angle of 45° to the vertical before reaching the lens-plate
system at the bottom. Light is reflected from the upper surface of the glass plate and the lower
surface of the lens. Due to the air film formed by the glass plate and lens, interference fringes are
formed, which are observed directly through a traveling microscope. The rings are concentric circles.
A dark central spot is obtained when viewed by reflection.

4 Theory
4.1 What are Newton’s Rings?
Newton’s rings are a series of concentric circular rings consisting of bright- and dark-colored fringes.
When a plano-convex lens lies on top of a plane lens or glass sheet, a small layer of air is formed
between the two lenses. Newton’s rings are formed by the interference phenomenon when monochro-
matic and coherent rays of light are reflected from the top and bottom surfaces of this air film. The
film’s thickness varies from zero at the point of contact to a finite value in the wedge-shaped region.

1
 Figure 1: Newton’s ring apparatus and pattern

4.2 Principle of Newton’s Rings Formation

The phenomenon of the formation of Newton’s rings can be explained based on the wave theory of
light.
• An air film of varying thickness is formed between the lens and the glass sheet.
• When a ray falls on the surface of the lens, it is reflected as well as refracted.
• When the refracted ray strikes the glass sheet, it undergoes a phase change of 180° on reflection.
• Interference occurs between two waves that interfere constructively if the path difference be-
tween them is (m + 12 )λ and destructively if the path difference between them is mλ, thereby
producing alternate bright and dark rings.

4.3 Derivation of the Equations

Consider a ray of light incident on the air film at a point where its thickness is t. The optical
path difference between the two reflected rays will be 2t. Taking into account the phase change of
180° for reflection at the rare to the dense surface, the conditions for constructive and destructive
interference are:

1
2t = (m + )λ (for constructive interference or bright rings) (1)
2
2t = mλ (for destructive interference or dark rings) (2)

where m is the order of the ring and can take the values m = 0, 1, 2, 3, . . . , n
If R is the radius of curvature of the lens and r is the distance of the point under consideration to

2
Figure 2: Schematic view of Plano-convex lens above a glass plate for derivation of the path difference

the point of contact of the lens and glass plate, then

R2 = (R − t)2 + r2 (Using Pythagoras theorem) (3)

2 2 2 2
R = R − 2Rt + t + r (4)
2 2
r D
=⇒ 2t = = (since t2 << r2 and D = 2r, the diameter of a ring) (5)
R 4R
Combining this result with the condition for the (p+n)th and pth dark rings. Then, the diameters
of the two rings are given by

2
Dp+n = 4R(p + n)λ (6)
Dp2 = 4Rpλ (7)

Subtracting the two equations and rearranging

2
Dp+n − Dp2 = 4Rnλ (8)
Thus, the radius of the Plano-convex lens R can be determined from this equation
2
Dp+n − Dp2
R= (9)
4λn
Equation 9 is the working formula for the experiment. By measuring the diameters of Dp and Dp+n
of pth and (p + n)th dark/bright rings and by knowing the wavelength λ of the light employed,
the radius of curvature R of the convex surface of the Plano-convex lens can be determined from
equation 9 where n is the difference of the ring numbers.

3
5 Procedure
1. The Newton’s rings are located by looking through the travelling microscope and its cross wire
is placed at the centre of the ring system by adjusting the screws of the microscope.
2. Carefully counting the number of rings, the cross wire is moved to the left hand (right hand)
side and is made tangential to the outer edge of the 13th dark ring. The readings of the linear
and circular scales are noted down.
3. The crosswire is then moved to its right (left) and made tangential to the 11th dark ring
and the readings noted as before. The process is repeated and the microscope moved inwards
towards the centre of the ring system till the 2nd dark ring.
4. The cross wire is next moved to the 2nd dark ring on the right hand (left hand) side and
readings taken down. The process is repeated and the microscope moved outwards till the
13th dark ring is reached on the right hand (left hand) side.
5. From the data entered in the table, the difference of the readings of the left and right hand
side of a particular ring gives the diameter of that ring.

6 Observation and Calculation

Least count of travelling microscope = ........cm

Figure 3: Table for Observational data of experiment

4
6.1 Graph
As can be seen in the working formula, the square of the diameter of the dark rings D2 has a linear re-
lationship with the ring number n. So, a best fit straight line is drawn passing through the origin that
best fits the data obtained from the table. The slope of the straight line so obtained D2 /n is graphi-

Calculation:
cally calculated and used in the working formula. λ= cm
2
From graph, D /n = cm2
R= cm

7 Precaution
1. The light source should be properly aligned with the Newton’s ring setup for maximum visi-
bility. Most importantly, the glass plate P has to be aligned properly until a uniformly bright
field is seen through the microscope.
2. As the first few rings are indistinct, it is very difficult to ascertain the exact ring number of
the first clearest ring.
3. The central indistinct rings should be avoided while taking readings.

8 Viva Q and A
1. Q.1. Why are Newton’s rings circular?
Ans. The plano-convex lens is circular. All the bright and dark fringes are the loci of the
points of the film of equal thickness. As the equally thick films are formed along the diameter
of the circular shape, the fringe pattern is also circular.
2. Q.2. Why is the center of Newton’s rings dark?
Ans. At the point of contact of the lens with the glass plate, the thickness of the air film
is minimal compared to the wavelength of light. Therefore, the path difference introduced
between the interfering waves is zero, the condition of minimum intensity. Consequently, the
interfering waves at the center are opposite in phase and interfere destructively.
3. Q.3. Why is sodium light used in Newton’s ring experiment?
Ans. Sodium light is used in Newton’s rings experiment because it is monochromatic, and
the two spectral lines of sodium can be resolved without difficulty.
1

1 Images and theory partially used from https://www.sciencefacts.net/newtons-rings.html