

NEWTON'S
RINGS


NEWTON'S
RINGS


When a planoconvex lens with its convex surface is placed on a plane glass sheet, an air film of gradually increasing thickness outward is formed between the lens and the sheet. The thickness of film at the point of contact is zero. If monochromatic light is allowed to fall normally on the lens, and the film is viewed in reflected light, alternate bright and dark concentric rings are seen around the point of contact. These rings were first discovered by Newton, that's why they are called NEWTON'S RINGS .  
WHY
NEWTON'S RINGS ARE FORMED



Newton's rings are formed due to interference between the light waves reflected from the top and bottom surfaces of the air film formed between the lens and glass sheet.  
EXPLANATION


The phenomenon of the formation of the  Newton's rings can be explained on the basis of wave theory of  
light. An air film of varying thickness is formed between the lens and the glass sheet. When a light ray is incident on the upper surface of the lens, it is reflected as well as refracted. When the refracted ray strikes the glass sheet, it undergo a phase change of 180^{O }on reflection. Interference occurs between the two waves which interfere constructively if path difference between them is (m+1/2)l and destructively if path difference between them is ml producing alternate bright and dark rings. 

RADIUS
OF RINGS


Let
the radius of curvature of the convex lens is R and the radius of
ring is 'r'. Consider light of wave length 'l'
falls on the lens. After refraction and reflection two rays 1 and
2 are obtained. These rays interfere each other producing alternate
bright and dark rings. At the point of contact the thickness of air film is zero and the path difference is also zero and as a 180^{O} phase change occurs, so they cancel each other and a dark ring is obtained at the centre. 

As we move away from the central point , path difference is also changed and alternate dark and bright rings are obtained.  
Let
us suppose that the thickness of air film is 't'. By using the theorem of geometry, 

r^{2}
= 2Rt.............. (1)


In thin films, path difference for constructive interference is:  
2nt
= (m+1/2) l


Where
n= refractive index For air n = 1 Therefore, 

2t
= (m+1/2) l .............. (2)


For
first bright ring m = 0 For second bright ring m = 1 For third bright ring m = 2 Similarly For N^{th} bright ring m = N1 

Putting the value of m in equation (2)  
2t
= (N1+1/2) l
2t = (N1/2)l t =1/2 (N1/2) l .............. (3) 

Putting the value of 't' in equation (1)  
r^{2}
= 2Rt
r^{2} = 2R . 1/2 (N1/2) l r^{2} = R (N1/2) l 

This
is the expression for the radius of N^{th} bright ring where r_{n} = radius of N^{th} bright ring N = Ring number R = radius of curvature of lens l = Wave length of light 

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