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Fundamentals of Wave Physics and Optics

Apr 25, 2025

Wave Physics Lecture Notes

Wave Basics

  • Wave Energy Transfer: All waves transfer energy without transferring matter.
  • Longitudinal Waves:
    • Oscillations are parallel to the direction of energy transfer.
    • Particles bunch up (compressions) and spread out (rarefactions).
  • Transverse Waves:
    • Oscillations are perpendicular to the direction of energy transfer.

Wave Forms and Measurements

  • Waveform Representation:
    • Displacement (y-axis) vs time or distance (x-axis).
    • Amplitude: Maximum displacement from equilibrium.
    • Wavelength (λ): Distance for one complete wave (in meters).
    • Time Period (T): Time for one complete wave to pass.
    • Frequency (f): Number of waves passing a point per second (Hz).
      • Relationship: ( f = \frac{1}{T} )
  • Wave Equation:
    • ( v = f\lambda ) (Wave speed = frequency × wavelength).

Light and Refraction

  • Visible Light Wavelengths: 400 to 750 nm.
  • Intensity and Amplitude: Intensity ( \propto ) amplitude².
  • Refraction:
    • Change in speed and wavelength when moving between mediums.
    • Refractive Index (n): ( n = \frac{c}{v} ) (c = speed of light in vacuum, v = speed in medium).
    • Snell’s Law: ( n_1 \sin \theta_1 = n_2 \sin \theta_2 ).
    • Critical Angle and Total Internal Reflection: ( \sin \theta_c = \frac{n_2}{n_1} ).

Optics and Lenses

  • Optic Fibers: Use total internal reflection with graded index fibers to minimize pulse broadening.
  • Lens Behavior:
    • Convex Lens: Converges light rays; forms real, inverted images.
    • Concave Lens: Diverges light rays; forms virtual images.
    • Lens Power: ( P = \frac{1}{f} ) (Diopters).
  • Polarization: Polarizing filters allow only certain orientations of light waves to pass.

Wave Interference

  • Progressive vs Stationary Waves:
    • Progressive Waves: Move through medium; points oscillate at different phases.
    • Stationary Waves: Formed by superposition of opposing waves; nodes and antinodes.
  • Phase Difference:
    • Measured in degrees or radians (0 or 360° = 2Ï€ radians).
    • Points in phase or anti-phase.

Young’s Double Slit Experiment

  • Coherent Light: Constant phase difference.
  • Interference Pattern: Bright (constructive interference) and dark (destructive interference) fringes.
  • Equation: ( W = \frac{\lambda D}{s} ) (W = fringe spacing, D = screen distance, s = slit separation).
  • Single Slit Diffraction: Wider central maximum and reduced intensity.

Diffraction Gratings

  • Grating Equation: ( n\lambda = d \sin \theta ).
    • Calculate maximum orders and visible orders based on grating.
  • Effects of Changes:
    • Changes in wavelength or grating spacing affect the order and visibility of patterns.

Summary and Practical Tips

  • Practical Work: Use lasers for precise monochromatic light and measure multiple fringes for accuracy.
  • Applications: Study these concepts for understanding wave behavior in physical systems and applications like optic fibers, lenses, and diffraction devices.

Full transcript