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Course Code: PHY-1102
Course Title: Physics I Lab
EXPT. NO. 4
DETERMINATION OF THE RADIUS OF CURVATURE OF A LENS BY
NEWTON’S RINGS
OBJECTIVE:
To determine the radius of curvature of a plano-convex lens using Newton's rings method
To gain familiarity with using a Vernier microscope.
THEORY:
Newton’s rings is a noteworthy illustration of the interference of light waves reflected from the
opposite surfaces of a thin film of variables thickness. When a Plano –convex lens L of the large
radius of curvature is placed on a glass plate P, a thin air film of progressively increasing thickness
in all directions from the point of contact between the lens and the glass plate is very easily formed
(Fig. 5.36).
The air film thus possesses a radial symmetry about the point of contact. When it is illuminated
normally with monochromatic light, an interference pattern consisting of a series of alternate dark
and bright circular rings, concentric with the point of contact is observed (Fig. 5.37). The fringes are
the loci of points of equal optical film thickness and gradually become narrower as their radii
increase until the eye or the magnifying instrument can no longer separate them.
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Let us consider a ray of monochromatic light AB from an extended source to be incident at the
point B on the upper surface of the film (Fig. 5.36). One portion of the ray is reflected from point B
on the air boundary and goes upwards along BC. The other part refracts into the air film along BD.
At point again reflected along EDF. The two reflected waves BC and BDEF are derived from the
same source and are coherent. They will produce constructive or destructive interference depending
on their path difference. Let e be the thickness of the film at the point E. Then the optical path
difference between two rays is given by 2µecos (θ+r) where θ is the angle which the tangent to the
convex surface at the point E makes with the horizontal , r is the angle of the refraction at the point
B and µ is the refractive index of the film with respect to air. From an analytical treatment by
Stokes, based on the principle of optical reversibility, and Lloyd’s single mirror experiment, it was
established that an abrupt phase change of π occurs when light is reflected from a surface back to a
denser medium while no such phase change occurs when the point is backed by a rarer medium
(air) when the D point is backed by a denser medium (glass). Thus there will be an additional path
difference of λ/2 between the rays BC and BDEF corresponding to this phase difference of π. Then
the total optical path difference between the two rays is
2µecos (θ+r) +_λ/2
The two rays will interfere constructively when
2µe𝑐o𝑠 (𝜃 + 𝑟) + _𝜆/2 = n λ
or, 2µe𝑐o𝑠 (𝜃 + 𝑟) = (2𝑛 + 1) λ/2 …… … (1)
The minus sign has been chosen purposely science n cannot have a value zero for the bright fringes
seen in reflected light. The rays will interfere destructively when
2µe𝑐o𝑠 (𝜃 + 𝑟) + _𝜆/2=(2𝑛 + 1)λ/2
or, 2µe𝑐o𝑠 (𝜃 + 𝑟) = 𝑛λ, .. … (2)
λ is the wave length in air.
In practice, a thin lens of extremely small curvature is used in order to keep the film enclose
between the lens and the plane glass place extremely thin. As a consequence the angle 𝜃 become
negligibly small as compare to r. furthermore, the experimental arrangement is so designed that the
light is indecent almost normally on the film and is and is viewed from nearly normal directions by
reflected light so that cause r=1. Accordingly eqns reduce to,
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2µe𝑐o𝑠 = (2𝑛−1)λ…
2
bright,
and 2µe = 𝑛λ … . . drak.
Let R be the radius of curvature of the convex surface which rest one the plane glass surface (Fig.
5.38). From the right angled triangle OFB1, we get the relation
𝑅2 = 𝑟2𝑛 + (𝑅 − e)2
Or 𝑟𝑛2 = 2𝑅e − e2
Where 𝑟𝑛 is the radius of the circular ring corresponding to the constant film thickness e. As, outline
above, the condition of the experiment makes e extremely small. So to a sufficient degree of
accuracy e^2 may be neglected compare to 2Re. then
𝑟2
𝑛.
e = 2𝑅
Substituting
the value of in the expressions for the bright and dark fringes, we have
𝑛λR
𝑟2 =
µ … . . 𝑏𝑟i𝑔ℎ𝑡
𝑛
2
and (2𝑛−1)λR
𝑟2 =
… … dark
𝑛
µ
The corresponding expressions for the squares of the diameters are,
𝐷2 =
2(2𝑛−1)&𝑅
𝑛
… . . 𝑏𝑟i𝑔ℎ𝑡
µ
And
𝐷2 =
𝑛
4𝑛&𝑅
… . 𝑑𝑎𝑟𝑘
µ
In the laboratory, the diameters of the Newton’s rings can be measured with a microscope. Usually
a little away from the centre, a bright or dark ring is chosen which is clearly visible and its diameter
measured. Let it be the nth order ring. For a air filmµ = 1. Then we have,
𝐷𝑛2 = 2(2𝑛 − 1)𝜆𝑅 … (3). . 𝑏𝑟i𝑔ℎ𝑡
and
𝐷𝑛2 = 4𝑛𝜆𝑅 … (4). 𝑑𝑎𝑟𝑘
The wavelength of the monochromatic light employed to illuminate the film can be computed from
either of the above equations, provide R is known.
However in actual practice another ring, p rings from this ring onwards is selected the diameter of
this (n+p)th ring is also measured. Then we have,
2
𝐷𝑛+𝑝
= 2(2𝑛 + 2𝑝 − 1)𝜆𝑅 … . . 𝑏𝑟i𝑔ℎ𝑡
and
2
𝐷𝑛+𝑝
= 4(𝑛 + 𝑝)𝜆𝑅 … . 𝑑𝑎𝑟𝑘
and 𝐷2 , we have
𝑛+𝑝
𝑛+𝑝
2
2
𝐷
− 𝐷 = 4𝑝𝜆𝑅 … … (5)
Subtracting 𝐷2
𝑛+𝑝
𝑛
for either bright or dark light.
𝑅=
𝐷𝑛+𝑝2−𝐷𝑛2
4𝑝𝜆
….
…. (6)
APPARATUS:




Two convex lenses one of whose radius of curvature is to be determined
Glass plate
Sodium lamp
Travelling microscope, etc.
PROCEDURE:
(i)
Arrange your apparatus as shown in Fig 5.39. Level the microscope so that the scale along which it slides is
horizontal and the axis of the microscope is vertical. Focus the eyepiece on the cross-wires. Determine the
venire constant of the micrometer screw of the microscope.
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(ii)
Carefully clean the surfaces of the lens L and the glass plate P by means of cotton moistened with benzene or
alcohol. Place the glass plate P as shown in the figure. Make an ink dot-mark on the glass plate and focus the
microscope on this dot. Now place the lens L on it in such a way that the centre of the lens, which is exactly
above the dot, is vertically below the microscope objective.
(iii)
Place the glass plate G in its position, as shown in the figure, in such a way that light from the source S, after
passing through the lens C, is incident on it at an angle of approximately 45 degree. If you now look into the
microscope, you will probably see a system of alternate dark and bright rings. Adjust the glass plate G by
rotating it about a horizontal axis until a large number of evenly illuminated bright and dark rings appear on
both sides of the central dark spot. Adjust the position of the lens C with respect to the flame so that a
maximum number of rings are visible through the microscope. This will happen when the flame will be at the
focal plane of the lens C.
(iv)
After completing these preliminary adjustments, focus the microscope to view the rings as distinctly as
possible and set one of the cross-wires perpendicular to the direction along which the microscope slides. Move
out the microscope to the remotest distinct bright ring on the left side of the central dark spot. The cross-wire
should pass through the middle of the ring and should be tangential to it. Note the reading of the microscope.
Move the microscope back again. Turn the screw always in the same direction to avoid any error due to
backlash. Set the cross-wire carefully on the centre of each successive bright ring and observe the microscope
reading. Go on moving the microscope in the same direction. Soon it will cross the central dark spot and will
start moving to the right side of it. As before set the cross-wire on the consecutive bright rings and take
readings. Proceed in this way until you have reached the same remotest bright ring as in the case of left side of
the dark spot. Considering a particular ring, the difference between the left side and right side readings, gives
the diameter of the ring. In this way, the diameters of the various rings are determined (see discussion).
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(v)
Tabulate the readings as shown below. While tabulating the reading you should be careful about the number of
the ring so that the left side and right side readings correspond to the same ring.
The whole experiment may be repeated moving the microscope backwards in the opposite direction over the
set of rings.
Draw a graph with the square of the diameter as ordinate and number of the ring as abscissa. The graph should
be a straight line.(fig.5.40)
From the graph determine the difference between the squares of the diameters of any two rings which are
separated by say about 10 rings i.e.. p is equal to 10. Now calculate R with the help of eqn. (6)
(vi)
(vii)
(viii)
DATA COLLECTION:
Vernier const, of the micrometer screw =
… mm
Table-1 for ring diameter
Ring
number
Reading of the microscope
Left side
Main
scale
reading
(S)
mm
Vernier
reading
(V)=VSR*V
C
mm
Total
reading=S+V
mm
Diamet
er of
the ring
(D=L~
R)
mm
Right side
Mean
mm
Main
scale
reading
(S)
mm
Vernier reading
(V)=VSR*VC
mm
Total
reading=S+
V
mm
D²
mm2
Mean
mm
CALCULATION:
Mean wavelength of sodium light =5893×10-8 cm
From
graph
2
2
2
𝐷
𝑛+𝑝
𝑅=
− 𝐷 = ⋯ … . 𝑐𝑚
𝑛
𝐷𝑛+𝑝2−𝐷𝑛2
4𝑝𝜆
….
=
… … cm
RESULT:
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The radius of curvature of the lower surface of the given lens= … cm
REPORT :
1. Show the results in tabular form.
2. Comment on the results obtained and discrepancies (if any).
CAUTIONS:
1. Take care of the reading of the apparatus.
2. Precaution should be taken so that the cross wire of the microscope remains fairly center of the
rings width especially for thick rings.
CONCLUSIONS:
The phenomenon of Newton's rings, named after Isaac Newton, is an interference pattern caused by
the reflection of light between two surfaces - a spherical surface and an adjacent flat surface. When
viewed with monochromatic light, it appears as a series of concentric, alternating light and dark
rings centered at the point of contact between the two surfaces. Using this apparatus, students can
observe the phenomenon of equal-thickness interference. By measuring interference fringe
separation, the radius of curvature of the spherical surface can be calculated. Using this apparatus
student can also measure the wavelength of the light used in this experiment.
QUESTIONS:
1.
2.
3.
4.
What is meant by interference of light?
Where are the rings formed?
Will the center rings be bright or dark?
Why do you use monochromatic light instead of white light?
REFERENCES:
 Practical Physics
By Dr. Giasuddin Ahmad and Md. Shahabuddin
Prepared & Edited By Dr. Md. Rafi Uddin
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