Wave Optics

• Wavefront and Huygens' Principle

  • Wavefront Definition: Locus of all points having the same phase
  • Types of Wavefronts
    • Spherical Wavefront: From a point source
    • Cylindrical Wavefront: From a linear source
    • Plane Wavefront: From a distant source (infinity)
  • Huygens' Principle
    • Every point on a wavefront acts as a source of secondary wavelets
    • New wavefront is the envelope of secondary wavelets at a later time
  • Reflection and Refraction
    • Proof of Laws of Reflection using Huygens' principle
    • Proof of Snell's Law of Refraction using Huygens' principle

• Interference of Light Waves

  • Superposition Principle: Net displacement is the vector sum of individual displacements
  • Coherent Sources
    • Same frequency and constant phase difference
    • Essential for sustained interference
  • Young’s Double Slit Experiment (YDSE)
    • Setup: Monochromatic light and two closely spaced slits
    • Constructive Interference (Bright fringes): Path difference $\Delta x = n\lambda$
    • Destructive Interference (Dark fringes): Path difference $\Delta x = (n + \frac{1}{2})\lambda$
    • Fringe Width ($\beta$): $\beta = \frac{\lambda D}{d}$

• Diffraction of Light

  • Definition: Bending of light around corners of obstacles/apertures
  • Types of Diffraction
    • Fresnel Diffraction: Source and screen are at finite distances
    • Fraunhofer Diffraction: Source and screen are effectively at infinity
  • Single Slit Diffraction
    • Central maximum (bright and wide)
    • Secondary maxima and minima
    • Condition for minima: $a \sin\theta = n\lambda$
  • Width of Central Maximum: $\frac{2\lambda D}{a}$
  • Resolving Power
    • Rayleigh's criterion for resolution
    • Resolving power of Microscope: $\frac{2\mu \sin\theta}{\lambda}$
    • Resolving power of Telescope: $\frac{D}{1.22\lambda}$

• Polarization of Light

  • Unpolarized Light: Vibrations in all directions perpendicular to propagation
  • Polarized Light: Vibrations restricted to a single plane (Transverse nature)
  • Methods of Polarization
    • Polarization by Reflection
    • Brewster's Law: $\mu = \tan i_p$ (Polarizing angle $i_p$)
    • Polaroids: Uses and applications (Sunglasses, LCDs)
    • Scattering of Light: Explains blue color of the sky and red sunset