Newton’s rings-Radius of the curvature of convex lens using Newton’s rings

 AIM:  To determine the radius of the curvature of the convex lens using Newton’s rings.

Newton’s rings

Superposition Principle: When two or more light waves arrive at a point simultaneously the intensity of the light at that point gets changed. If the light waves arrive in phase (i.e. having zero phase difference) then the point appears bright while if they arrive out of phase, (i.e. with 180⁰ phase difference then the point appears dark. Thus a pattern of bright and dark points is obtained

APPARATUS: Source of monochromatic light (sodium light), two plane glass plates, Plano-Convex lens, traveling microscope.     

               

FORMULA:                                  R = m/4 l                                                                  

Where m = slope of the line obtained by plotting the squares diameters of rings against

                       number of rings.

               R = radius of curvature of the convex lens.

INTRODUCTION:

 Superposition Principle: When two or more light waves arrive at a point simultaneously the intensity of the light at that point gets changed. If the light waves arrive in phase (i.e. having zero phase difference) then the point appears bright while if they arrive out of phase, (i.e. with 180⁰ phase difference then the point appears dark. Thus a pattern of bright and dark points is obtained. The phenomenon in which the intensity at points in space varies due to superposition of two or more waves is called Interference. If the intensity is high the interference is called constructive while if the intensity is zero then it is called destructive interference. This pattern remains steady and observable if the phase difference between the two waves remains same w.r.t. time. Such waves for which the phase difference remains either same or zero are called coherent waves.

The phenomenon of interference can easily be observed if light is allowed to pass through a film bounded by two surfaces. A ray of light gets refracted when it travels from one medium to other. When the light passes through a film bounded by two surfaces it gets partially reflected and transmitted at two boundaries. The rays, which get reflected from the upper and lower surfaces, travel with different paths introducing a phase difference between them before they come out from same surfaces (see fig).

                                                

After coming out of the film they superpose with each other giving a pattern of alternate dark and bright straight fringes. Since the film is of equal thickness; the fringes are of equal thickness and parallel.     

From fig; the path difference,  D =(BE + ED) – (BC + λ/2)

The λ/2 term appears due to the fact that ray BC gets reflected from denser medium. From geometry; BE = ED =  ( t /cos r)

so optical path is μ( t /cos r)

BC = BD sin i = 2 t tan r

Putting these values; D = 2 μ t cos r - λ/2.

For brightness; D= n λ                  i.e. 2 μ t cos r = (2n+1) λ/2.

For darkness ;  D= (2n + 1)λ/ 2           i.e. 2μ t cos r = n λ.

NEWTON’ RINGS: This is another arrangement for obtaining the interference pattern. In this arrangement an air film is formed on placing a Plano convex lens on plane glass plate as shown in fig. The film formed is a circular wedge shaped film with a variable thickness. At point of contact; the thickness is zero and the thickness increases on either side of the point of contact. Locus of points of equal thickness is thus a circle. Hence the fringes are circular. At the center since the thickness is zero; the spot appears dark.

thus r_n µ Ön; or diameter d_n² = 8 R n λ          

            THEORY:  let PQ be section of plano convex lens with radius of curvature R.

                                                          Let n^th dark ring is formed at film thickness t.                                                  let r be the radius dark ring From fig :   AC x CB = r x r   

                                                                          i.e. (2R- t)t = r x r

                                                                                      i.e.                                    2Rt =  r²;     neglecting t².

                                                                                     So r = Ö2Rt      -------------(1)

                                                           then for the dark ring  2μt cos r = n λ                                      

                                                      for air μ =1& for normal incidence cos r =1                                                                                        so  t = n λ                                        

                                                   putting this value in (1);    r = Ö2R n λ

                                                        thus r_n µ Ön; or diameter d_n² = 8 R n λ

                                                          so λ = (d_n² /n)x 8 R

                                                 A straight line is obtained if ‘d²’ is plotted against

                                                 The slope ‘m’ of this line is given

                                                                               d_n+p² -  d_n ² 

                                                                                        p           

                                         hence the value of  R can be given as                                                                                                             m

                                                       R =    

                                                                                         4 l

PROCEDURE:

 1. The least count of microscope is found.

 2. Newton’s ring assembly is placed at normal incidence of light.

 3. Focus microscope at central dark spot. Note down reading .

 4. Microscope is  moved in one direction till it crosses 20^th dark ring.

 5. It is then moved in backward direction up to 15^th ring. Vertical cross wire is made

     tangential to this ring. Note down microscope reading.

6. The above procedure is repeated for 13^th, 11^th …. etc rings.

7. Microscope is further moved till it reaches at15^th ring on reverse direction.

8. Steps 5 and 6 are repeated for reverse side.

9. Difference between readings on two sides gives diameters of rings.

PRECAUTIONS:

1. Assembly should be arranged for normal incidence carefully.             
2. The glass plate and lens should be clean so that no additional path difference is introduced due to dust.

RESULT:  The radius of curvature of plano covex lens is found to be  -------

Answer the following

Q1. Why is the central spot dark?

Q2. If the radius of the 10^th ring is 0.1 cm then what is the diameter of 20^th ring?

Q3. Give an example of interference in sound waves?

Q4. For what wavelength the diameters of rings are double than you have obtained?

Q5. Define interference.

Q6. How the rays are incident normally on the assembly?

Q7. Can you use bright rings instead of dark rings?

Q8. If the lens of larger diameter is used, what change is observed in diameters of rings?

Q9. Mention few applications of Newton’s ring.

Q10. Under what conditions you observe coloured rings?

Q11. State superposition principle.

Q12. Why the sources should narrow?

Q13. How will you find the refractive index of liquid?

Q14. Can you use X-rays for this arrangement for getting interference pattern?

Q15. Under what conditions bright central spot is observed?

Q16.How the least count of traveling microscope is calculated?

Q17. Is the least count of spectrometer and microscope is same? Justify.

Q18. Sometimes the fringes are not perfectly circular? What is the reason?

Q19. What are the engineering applications of Newton’s rings?

Q20. What is the role of inclined glass plate kept in the path of light? At what angle should it be arranged?