Name of the Experiment
To determine the wavelength of monochromatic light by
Newton’s rings.
Objectives
➢ To measure the radius of curvature of a given convex lens.
➢ To observe the interference of light and learn how this pattern helps to determine the
wavelength of monochromatic light.
Theory
The phenomenon of Newton's rings is an interference pattern caused by the reflection and
transmission of light between a spherical surface and an adjacent flat surface which form air thin
film. When viewed with monochromatic light as shown in Fig. a, it appears as a series of concentric,
alternating bright and dark rings as shown in Fig. b centered at the point of contact between the two
surfaces.
The two reflected rays BC and DF from the top and bottom of the air film are produced through division of
amplitude from the same incident ray AB and are, therefore, coherent. Hence, they will interfere and
produce a system of alternate dark and bright rings, as shown in Fig. C.
The optical path difference (∆) between the rays BC and DF is given by
∆= 2𝜇𝑡𝑐𝑜𝑠𝑟 − 𝜆/2 = 2𝑡 – 𝜆/2 … … … … … . (1)
Where, 𝑡 is the thickness of the air film, 𝑟 is the angle of refraction (the angle between the refracted ray BD
and normal BG). Here, for normal incident, r = 0 and therefore, 𝑐𝑜𝑠𝑟 = 1; in case of air, the refractive index,
𝜇 = 1.
According to the condition of interference,
For bright rings, 2𝑡 – 𝜆/2 = 𝑛𝜆 (where 𝑛 = 1, 2, 3 … ), i.e., 2𝑡 = (2𝑛 + 1) 𝜆/2 …………. (2)
For dark rings, 2𝑡 – 𝜆/2 = (2𝑛 + 1) 𝜆/2 (where 𝑛 = 1, 2, 3 … ), i.e., 2𝑡 = 𝑛𝜆 ………….. (3)
Fig. D shows that the plano-convex lens appears as part of circle of radius R known as the radius of curvature
of this lens.
If 𝑟n is the radius of the nth dark ring created for air film having thickness, 𝑡, then from the triangle AOB,
𝑅2 = 𝑟n2 + (𝑅 − 𝑡)2 … … … (4)
Since 𝑅 ≫ 𝑡, 𝑡2 can be neglected and then Equation (4) becomes
𝑟𝑛2
𝑡= … … … … … (5)
2𝑅
Combining Equations (3) and (5), we can write for dark ring, 𝑟n 2 = 𝑅n𝜆
So, for the diameter of the 𝑛 𝑡ℎ ring (𝐷𝑛 ), can be expressed as, 𝐷n2 = 4𝑅n𝜆 … … … … (6)
For the diameter of the (𝑛 + 𝑝) 𝑡ℎ rings (𝐷𝑛+𝑝), 𝐷n+p 2 = 4𝑅 (n + p) 𝜆 … … … … … (7)
From Equations (6) and (7), we can write
2
𝐷𝑛+𝑝 − 𝐷𝑛2
𝜆=
4𝑝𝑅
Apparatus
Two convex lenses, glass plate, sodium lamp, travelling microscope, Vernier scale etc.
Procedure
(i) Found the least count of vernier scale.
(ii) Cleaned the surface of glass plate,and the Plano-convex lens, Put them in position as shown in Fig. a in
front of the sodium lamp.
(iii) Switched on the sodium lamp and saw that only parallel beam of light coming from the convex lens on
the glass plate.
(iv) Adjusted the position of microscope so that it lies vertically above the center of lens. Focused the
microscope so that alternate dark and bright rings are clearly visible.
(v) Adjusted the position of the microscope till the point of intersection of the cross–wires coincides with
the center of the ring system and one of the vertical cross-wires is perpendicular to the horizontal scale.
(vi) Moved the microscope so that the vertical cross wire lies tangentially at one of the extreme ends of the
6th dark ring.
(vii) Noted the reading of the scale reading of the microscope.
(viii) Slided the microscope backward with the help of screw and go on noting the readings when the cross
wire lies tangentially at the extreme ends of horizontal diameter of 6th, 5th, 4th, 3rd, 2nd and 1st dark rings
in column ‘Left (a)’ respectively.
(ix) Continued sliding the microscope to the right and noted down the readings in column ‘Right (b)’
when the vertical cross wires lies tangentially at the other extreme end of the diameter of 6th, 5th, 4th, 3rd,
2nd and 1st dark rings in respectively.
Data Collections
Ring Reading of the microscope Diameter D2
No Left Side Right Side of the
Main Vernier Total Mean Main Vernier Total Mean ring [D =
scale reading reading (L) scale reading reading (R) L ~ R]
reading (V) = =S+V reading (V) = =S+V
S cm vernier cm S cm vernier cm
division division
X V.C X V.C
cm cm
6
5
4
3
2
1
Table: Data for ring diameter.
Calculations
2
From the graph, 𝐷𝑛+𝑝 − 𝐷𝑛2 = ………….cm2
Radius of curvature of the lens, R = …………cm
Results
2 −𝐷2
𝐷𝑛+𝑝 𝑛
𝜆= 4𝑝𝑅
= ………………..A.U
Discussions
a) The intensity of the ring system decreased as one goes from the inner to the outer rings, thus
setting a limit for the selection of the outermost ring whose diameter was to be measured.
b) Newton's rings also be observed in transmitted light but in that case the rings would be less clearly
defined and less suited for measurement.
c) It is noticed that the inner rings were somewhat broader than the outer ones. Hence while
measuring the diameter of the inner rings some error be introduced. The cross-wire should be set
mid-way between the outer and inner edges of a ring. A more correct procedure was to determine
the inner and outer diameters of a particular ring by setting the cross-wire tangentially at the inner
and outer edges on both sides of the ring. From this the mean diameter was found.
d) The first few rings near the centre be deformed due to various reasons. The measurement of
diameters of these rings avoided.
e) Due account taken of the fact that in the present experiment, the rings which were formed in the
air film in the space between the lens and the glass plate were not seen directly but after refraction
through the lens. This inevitably introduces an error. However, the lens used is thin then this error
was not great.
Prepared by
Md. Mahabubul Imam Majumder
Lecturer of Physics
Mymensingh Engineering College, Mymensingh
Contact No: +8801635625069
Email: mahbub@mec.ac.bd; link2mahbub@gmail.com
