Newtons Rings Experiment

The Newtons Rings Experiment is clearly explained in this video.
Aim: To determine the wavelength of sodium light using Newton rings set up.
Objectives: To understand the phenomenon of interference in thin films by studying Newton’s ring pattern and determining the wavelength of light used.
Apparatus: optically flat  glass plate,  plano convex lens of large focal length, traveling microscope, sodium vapour lamp, spherometer etc.
Theory: When a plano convex lens of large focal length is placed on a glass plate such that its convex surface is in contact with the glass plate, then air film of gradually increasing thickness is formed between the two. At the point of contact the thickness of air film is zero. Monochromatic light whose wavelength is to be determined is allowed to fall normally on this assembly. To get normal incidence we keep the glass plate at an angle of 450 to the incident light. The thin air film is viewed in the reflected light with a traveling microscope and a pattern of concentric dark and bright rings is observed. These rings are known as Newton Rings.
Newton ring pattern is the interference pattern formed between the two rays reflected by the top and bottom surface of the air film formed between plano convex lens and optically flat glass plate. The rings are circular in nature because the thickness of the air film is constant along the circle. The central spot is dark as at the point of contact between planoconvex lens and optically flat glass plate, the thickness of the air film is zero.
Formulae:
                               D^2m+n ― D^2 n        slope    
             λ  =  -----------------------------  =  ---------------
                  4 M R                      4R
  where,
  M = 10
   R = Radius of curvature of plano-convex lens
   λ = wave length of monochromatic light
    Dm+n , Dn  are the diameters of (m+n)th & nth  dark ring respectively
    (difference between (m+n) & n )
Procedure:
1. Clean the optically flat glass plate and lens to remove the dust.
2. Set up the arrangement as shown in the diagram.
3. Focus the cross wires of travelling microscope on the rings.
4. Using the slow motion screw move the travelling microscope to the left, counting the rings, till the cross wires are tangential to the 30thdark ring.
5. Note down the position of the 30th ring on the travelling microscope.
6. Move the travelling microscope using the slow motion screw till the cross wires are tangential to the 25th ring.
7. Note down the position of 25th ring and so on for 20th, 15th, 10th, 5th and  0th  dark ring.
8. Keep the sense of motion in same direction i.e. towards right. Make the cross wires tangential to the other side of 0th dark ring. Note down its position.
9. Continue in this manner for 5th,10th , 15th,  20th ,  25th  & 30th  dark ring.
10. The difference between the left and right hand side positions of the respective rings will give their respective diameters. Measuring the value of radius of curvature, R, we can determine the wavelength of the source.
11. A graph is plotted between the diameter squares and the number of the ring. We can also determine the wavelength from the slope of the  graph.



Observations:
Least count of Travelling Microscope = 0.01 mm

Results:

The value  of  wavelength  of  sodium  vapour lamp
(from calculations)=
(from graph) =  



Conclusion:  Phenomenon of interference is understood with the help of Newton’s Ring set up.



Questions and Discussion:
1. What are Newton rings?
  Newton rings are interference pattern in the form of concentric bright and dark rings, first seen by Newton.
2.  Why are the rings circular?
   Rings are circular because the locus of all the points, having the same path difference, lie on a circle. The rings are not equi-spaced as the curvature of the lens increases non linearly. Hence rings at the center are well spaced, and crowded away for it.
3. Why do we take a plano convex lens of large R.
Lens of large R implies that thickness of air film formed between the plano convex lens and glass plate is small, which is the necessary condition for interference.
4. Why do we take the difference in diameters?
At the center of the rings is a dark spot, which corresponds to zero thickness (t~0) or condition for destructive interference. The number of rings present in the central dark spot cannot be counted. So to change the dependence of the equation from the number of the ring, to the number of rings between two reference rings, we take the difference between the diameters.
5. Why is the incidence normal?
 For normal incidence we can conveniently  place the detector/travelling microscope. It also simplifies the calculations.
6.What are the applications of Newton rings
Phenomenon of interference is used to determine the refractive index of a liquid which finds application in  pharmaceutical industries . It helps in determining the thickness of transparent films