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Understanding Waves in A-Level Physics

May 22, 2025

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Hall of AQA Waves for A-Level Physics

Oscillations and Waves

  • Amplitude: Maximum displacement from the equilibrium position.
  • Frequency: Number of completed cycles per unit time. Formula: ( f = \frac{1}{T} ).
    • SI Unit: Hertz (Hz), cycles per second.
  • Wavelength: Minimum distance between two points in a wave that are in phase.
  • Wave Speed: Distance traveled by the wave per unit time. Formula: ( v = f \lambda ).

Phase of a Wave

  • Describes the fraction of a cycle covered up to that point.
  • Measured in degrees or radians.
    • One complete cycle: 360° or 2Ï€ radians.
  • Phase Difference: Measure of how far out of sync two points on a wave are, expressed in degrees or radians.
    • Formula for phase difference: ( \text{Phase difference} = \frac{d}{\lambda} \times 2\pi ) (in radians).

Types of Waves

  • Transverse Waves: Oscillations are perpendicular to the direction of energy transfer.
    • Examples: Electromagnetic waves.
  • Longitudinal Waves: Oscillations are parallel to the direction of energy transfer.
    • Examples: Sound waves.

Polarization

  • Only transverse waves can be polarized.
  • Plain Polarized Wave: Oscillations are restricted to a single plane.
  • Applications: Polaroid materials absorb horizontal component; used to reduce glare.

Interference and Superposition

  • Superposition: Resultant displacement is the vector sum of individual displacements.
  • Path Difference: Difference in path lengths between waves from sources.
  • Coherence: Waves have constant phase difference and same frequency.

Young’s Double Slit Experiment

  • Demonstrates wave nature of light using interference patterns.
  • Fringe Separation Formula: ( W = \frac{\lambda D}{s} ).

Diffraction

  • Definition: Spreading of light as it passes through a gap or around an obstacle.
  • Single Slit Diffraction Pattern: Wide central maximum with narrower side fringes.
  • Diffraction Grating Equation: ( d \sin \theta = n \lambda ).

Refraction

  • Refractive Index: Ratio of speed of light in vacuum to speed in substance.
    • Formula: ( n = \frac{c}{v} ).
  • Total Internal Reflection: Occurs when light is completely reflected within a substance.
    • Critical Angle: Angle of incidence above which total internal reflection occurs.
    • Formula: ( \sin \theta_c = \frac{n_2}{n_1} ).

Fiber Optics

  • Core: Propagates light by total internal reflection.
  • Cladding: Provides protection and boundary for total internal reflection.
  • Dispersion: Material and modal dispersion can affect signal.

Essential Equations and Concepts

  • Wave Equation: ( v = f \lambda )
  • Snell’s Law: ( n_1 \sin \theta_1 = n_2 \sin \theta_2 )
  • Young’s Equation: ( W = \frac{\lambda D}{s} )
  • Diffraction Grating: ( d \sin \theta = n \lambda )
  • Critical Angle: ( \sin \theta_c = \frac{n_2}{n_1} )

Practical Applications

  • Laser Safety: Avoid shining lasers at people or reflective surfaces.
  • Uses of Diffraction Gratings: Identifying elements, studying crystal structures.

This summary covers the essential concepts and equations related to waves, polarization, interference, diffraction, refraction, and fiber optics in A-Level Physics. Use this as a reference for understanding wave phenomena and solving related problems.

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