Thursday 2 June 2011

Newton's Rings


Circular interference formed between a lens and a glass plate with which the lens is in contact. There is a central dark spot around which there are concentric dark fringes.The radius of the nth ring is given by . Where λ is the wavelength and R is the radius of curvature of the lens. 
a


      When a Plano convex lens of long focal length is placed in contact on a plane glass plate (Figure given below), a thin air film is enclosed between the upper surface of the glass plate and the lower surface of the lens. The thickness of the air film is almost zero at the point of contact O and gradually increases as one proceeds towards the periphery of the lens. Thus points where the thickness of air film is constant, will lie on a circle with O as center.
        By means of a sheet of glass G, a parallel beam of monochromatic light is reflected towards the lens L. Consider a ray of monochromatic light that strikes the upper surface of the air film nearly along normal. The ray is partly reflected and partly refracted as shown in the figure. The ray refracted in the air film is also reflected partly at the lower surface of the film. The two reflected rays, i.e. produced at the upper and lower surface of the film, are coherent and interfere constructively or destructively. When the light reflected upwards is observed through microscope M which is focused on the glass plate, series of dark and bright rings are seen with center as O. These concentric rings are known as " Newton's Rings ".
      At the point of contact of the lens and the glass plate, the thickness of the film is effectively zero but due to reflection at the lower surface of air film from denser medium, an additional path of λ/2 is introduced. Consequently, the center of Newton rings is dark due to destructive interference.
   Fig  . Experimental arrangement for observing Newton's rings
      Let us consider a system of plano-convex lens of radius of curvature R placed on flat glass plate it is exposed to monochromatic light of wavelength λ normally.
         The incident light is partially reflected from the upper surface of air film between lens and glass and light is partially refracted into the film which again reflects from lower surface with phase change of 180 degree due to higher index of glass plate. Therefore the two parts of light interfere constructively and destructively forming alternate dark and bright rings. 
      Now consider a ring of radius r due to thickness t of air film as shown in the figure given below:
      According to geometrical theorem, the product of intercepts of intersecting chord is equal to the product of sections of diameter then,

As t is very small then will be so small which may be neglected, then,


                                           
Radius for bright ring

The condition for constructive interference in thin film is,

                   m = 0,1,2,....

From equation (1) putting the value of t in the above equation we get,

                       
since n = 1 for air film
                                               
or
                             

For first bright ring, m = 0

For second bright ring, m = 1

For third bright ring, m = 2
Similarly, for Nth bright ring,
m = N - 1
                               
Radius for dark ring


The condition for destructive interference in thin film is,

2tn = mλ                                   m = 0,1,2,....
By putting the value of t, we get,

For air n = 1
                                   
 For   i.e. point of contact.

Now, if the radius of curvature of plano-convex lens is known and radius of particular dark and bright ring is experimentally measured then the wavelength of light used can be calculated from equation (3) and (4).

         Images of  Newton's Rings         s

Newton's Ring Apparatus
Picture from PHYWE
Picture from PHYWE
Picture from AMRITA

Video for Newton's Rings



27 comments:

  1. Can newton's ring form with transmitted if yes then please show the diagram how the instruments will be placed ?

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  3. if we replace the glass plate by a mirror .then the rings will be formed or not ????

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  5. why there is bright point at center?

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    1. There's no bright ring at center but a dark one due to interference of waves reflected from upper and lower surface of air film having phase difference of 180°. Phase difference occurs as a result of path difference of λ/2 due to higher refractive index of glass....That's what they say😇

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    2. That's what they say😇

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  6. It is perfectly a student friendly video.so helpful.thanks a lot!!!!

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  7. It is perfectly a student friendly video.so helpful.thanks a lot!!!!

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  8. When the ray falls on the top surface of the plano convex lens,many beams will form due to reflection and refraction at each surface. But we only consider the rays from the wedge shaped film to take part in superposition. What about the other rays??

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  9. Hi There
    Nice blog!
    Guys you can visit here to know more
    O rings

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  10. What happens to the light reflected from the upper surface
    of lens and lower surface of glass plate?

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  11. what kind of circular rings are form in newton ring experiment explain?

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  12. This comment has been removed by the author.

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  13. If why dark spot is formed at center

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  14. What will happen to central spot when pattern observe in transmitted light

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  15. Nice video and nice explanation itis very helpful to Student

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  16. IMPRESSED WITH SUCH A GOOD CONTENT!!
    VERY INTERESTING
    GREAT WORK
    Interference Analysis

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  17. Explain how Newton's rings are useful to find the flatness of a surface

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  18. In exam we will not do the derivation for the dark radius circle plz tell me tomorrow is my test

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