Wave Optics and its Key Points

Introduction to Wavefront

• Definition: A wavefront is every position of any wave equation where the phase is the same.
• Types:
  • Spherical Wavefront: For a point source.
  • Cylindrical Wavefront: For a linear source (like a tube light).
  • Planar Wavefront: For a light source at infinity.

Huygens’ Principle

• Every point on a wavefront behaves like a new light source.
• Secondary waves spread out in all directions and create new wavefronts.

Superposition Principle

• When two or more waves meet, they lose their individual identities and form a new wave.
• The resultant displacement is equal to the vector sum of the waves.

Interference of Light

• Coherent Light Source: Same frequency and zero or constant phase difference.
• Conditions:
  1. Frequency should be the same.
  2. Phase difference should be zero or constant.
• Maxima and Minima:
  • Maxima: Constructive interference (phase difference 2nπ)
  • Minima: Destructive interference (phase difference (2n+1)π)
  • Relation between path difference and phase difference: Δφ = (2π/λ) * Δx

Young's Double Slit Experiment

• Creating double slits from a single light source and observing the interference pattern on the screen.
• Path difference for maxima: nλ and phase difference 2nπ
• Path difference for minima: (2n+1)λ/2 and phase difference (2n+1)π
• Resultant intensity formula:
  • I = I₁ + I₂ + 2√(I₁I₂) cos φ

Diffraction of Light

• Bending and spreading of light when it passes by edges.
• Fraunhofer Diffraction: Single slit diffraction using a plane wavefront.
• Intensity Distribution:
  • Central maxima with the highest intensity.
  • Determination of positions of secondary maxima and minima.
• Conditions:
  • Secondary maxima: (a sin θ = (n+1/2)λ)
  • Minima: (a sin θ = nλ)