PROJECT

DATE CLIENTDECEMBER 2011 PHYSICS 3

NEWTON’S RINGS IV- Tau: Group I

What is it?

an interference pattern caused by the reflection of light between two surfaces -- a spherical surface and an adjacent flat surface

the basics: INTERFERENCE

Interference occurs between the two waves that interfere constructively if path difference between them is (m+1/2)and destructively ifpath difference between them is m

when viewed by monochromatic light...

a series of concentric, alternating bright and dark rings centered at the point of contact between the two surfaces

when viewed by white light...

concentric ring pattern of rainbow colors because the different wavelengths of light interfere at different thicknesses of the air layer between the surfaces

other observations

light rings = constructive interference between light rays reflected from both surfaces

dark rings = destructive interference

Also, the outer rings are spaced more closely than the inner ones.

DiagramWhen a plano-convex 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.

http://www.citycollegiate.com/newtons_rings.htm

what REALLY happens Formation: 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 of Phenomenon: (on basis of wave theory of light)

1. An air film of varying thickness is formed between the lens and the glass sheet.

2. When a light ray is incident on the upper surface of the lens, it is reflected as well as refracted.

3. When the refracted ray strikes the glass sheet, it undergoes a phase change of 180O on reflection.

derivation of the formula

R - radius of curvature of convex lens

r - radius of ring

l - wavelength of light

After reflection and refraction, 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 and the path difference both = 0. As a 180O path difference occurs, they cancel each other and a dark ring is obtained at the centre.

derivation of the formula

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,

derivation of the formulaIn thin films, path difference for constructive interference is:

2nt = (m+1/2)

 (where n is the refractive index, but since we’re dealing with air)

 

  2t = (m+1/2)

For first bright ring m = 0

For second bright ring m = 1

For third bright ring m = 2

For Nth bright ring m = N-1

Putting the value of m in equation 2

2t = (N-1/2)

         t =1/2 (N-1/2)

Putting the value of 't' in equation 1

r2 = 2Rt

r2 = 2R . 1/2 (N-1/2)

r2 = R (N-1/2)

Major Formula:

This is the expression for the radius of Nth bright ring where:

rn = radius of Nth bright ringN = Ring numberR = radius of curvature of lens = Wave length of light

more on the theory involved

Moving outwards from one dark ring to the next increases the path difference by the same amount λ, corresponding to the same increase of thickness of the air layer λ/2.

Since the slope of the convex lens surface increases outwards, separation of the rings gets smaller for the outer rings. For surfaces which are not convex, the fringes will not be rings but will have other shapes.

supplements for learning

http://scienceworld.wolfram.com/physics/NewtonsRings.html

http://www.youtube.com/watch?v=PU-SeNfIRcs

http://www.citycollegiate.com/newtons_rings.htm