Unit 4: Waves and Optics (Interference & Diffraction)

1. Interference of Light: Division of Wavefront & Amplitude

Interference is the phenomenon where two or more waves superimpose to form a resultant wave of greater, lower, or the same amplitude. To observe stable interference, light sources must be coherent (having a constant phase difference).

Methods of Producing Coherent Sources

• Division of Wavefront: The wavefront is divided into two parts by using slits, mirrors, or prisms. Examples include Young's Double Slit and Fresnel’s Biprism.
• Division of Amplitude: The amplitude of a single beam is divided by partial reflection and partial refraction. Examples include Newton's Rings and Michelson Interferometer.

2. Young's Double Slit Experiment (YDSE)

YDSE demonstrates the wave nature of light. A monochromatic light source illuminates two closely spaced slits (S1 and S2), producing an interference pattern of bright and dark fringes on a distant screen.

Fringe Width (β)

The distance between two consecutive bright or dark fringes is constant and given by:

Where:
λ = Wavelength of light
D = Distance between slits and screen
d = Distance between the two slits

3. Newton's Rings

When a plano-convex lens is placed on a flat glass plate, a thin film of air is formed between them. This film has a variable thickness. When monochromatic light is reflected from this film, circular interference fringes called Newton's Rings are observed.

Diameter of Rings

• Bright Rings: The diameter Dn is proportional to √(2n-1).
• Dark Rings: The diameter Dn is proportional to √n.

Determination of Wavelength (λ)

Using the diameters of the nth and (n+p)th dark rings:

Where R is the radius of curvature of the plano-convex lens.

4. Diffraction of Light: Fresnel vs Fraunhofer

Diffraction is the bending of light around the corners of an obstacle or aperture into the region of geometrical shadow.

5. Fraunhofer Diffraction at a Single Slit

When a plane wavefront is incident on a narrow slit of width 'e', the light is diffracted. A lens focuses these rays on a screen.

Condition for Minima

Where n = 1, 2, 3... represents the order of the minima. The central maximum is twice as wide as the secondary maxima.

6. Plane Transmission Grating

A diffraction grating is an optical component with a periodic structure (thousands of lines per cm) that splits light into several beams travelling in different directions.

Grating Equation

Where (e + d) is the Grating Element, θ is the angle of diffraction, and n is the order of the spectrum.

7. Resolving Power of Optical Instruments

The Resolving Power is the ability of an instrument to show two closely spaced objects as separate.

• Rayleigh's Criterion: Two images are just resolved when the central maximum of one diffraction pattern falls on the first minimum of the other.
• Resolving Power of Grating: Defined as λ / dλ = n * N (where N is the total number of lines).