Newton's Rings: Theory, Derivation, and Applications

Newton's Rings are concentric circular bright and dark rings formed due to interference between light waves reflected from the upper and lower surfaces of a thin air film.

Theory of Newton's Rings

When monochromatic light falls on the thin air film formed between the plano-convex lens and a glass plate, two reflected rays are produced:

• One from the upper surface of the air film.
• Another from the lower surface of the air film.

These reflected rays interfere with each other:

• Constructive interference produces bright rings.
• Destructive interference produces dark rings.

Thus, alternate bright and dark concentric circular rings are formed.

Determination of Refractive Index of a Liquid

When a liquid is introduced between the lens and the glass plate, the air film is replaced by a liquid film. Due to the increase in the refractive index, the diameter of the rings decreases. Let:

• D_a = diameter of the ring in air
• D_l = diameter of the ring in liquid

Then, the refractive index of the liquid (μ) is given by:
___
Thus, by measuring the diameter of the rings before and after introducing the liquid, the refractive index of the liquid can be calculated.

Derivation of Diameter Relation

For dark rings, the path difference condition is: _____. From the geometry of the lens: ___. Substituting t: _______ _______ _________. Since diameter D_n = 2r_n, we square both sides _____________ to get: ___________.

Hence Proved: The square of the diameter of the n-th dark ring is directly proportional to the natural number n.

Applications of Newton's Rings

1. Determination of the wavelength of light.
2. Determination of the refractive index of a liquid.
3. Testing the flatness/optical smoothness of surfaces.

Experimental Arrangement and Diameter Relation

Q. Describe the experimental arrangement for producing Newton's rings by reflected light and show the diameter relation?

Ans. Definition: Newton's Rings are concentric circular bright and dark rings formed due to interference between light waves reflected from the upper and lower surfaces of a thin air film.

Experimental Arrangement

The apparatus consists of:

• Plano-convex lens
• Glass plate
• Monochromatic light source
• Microscope

• The plano-convex lens is placed on a flat glass plate, forming a thin air film of varying thickness.
• Monochromatic light falls normally on this setup.
• Interference takes place between rays reflected from the upper surface of the air film and the lower surface of the air film.
• As a result, concentric circular rings are formed.