3. Waves

• Displacement: The distance and direction of a particle from the equilibrium position
• Longitudinal and Transverse Waves:

  • Transverse waves: Waves whose oscillations are perpendicular to the direction of propagation of energy (e.g. electromagnetic waves)
  • Longitudinal waves: Waves whose oscillations are parallel to the direction of propagation of energy, consisting of compressions and rarefactions
  • Only transverse waves can be polarised, meaning all waves oscillate in the same plane
• Superposition and Interference:

  • Waves meet at superposition, where the total displacement at a point is the sum of individual displacements
  • Constructive interference occurs when waves are in phase, resulting in peaks or troughs combining
  • Destructive interference occurs when waves are in antiphase, canceling each other out
  • Stationary waves store energy instead of transferring it
• Waves on a String:

  • A stationary wave is formed on a string fixed at both ends
  • Constructive interference at places in phase creates antinodes, while destructive interference at places in antiphase creates nodes
  • The fundamental frequency of a wave on a string can be found using the given equation
• Double Slit Interference:

  • Young's Double Slit Experiment shows interference pattern from coherent wave sources
  • Diffraction is the spreading out of waves when passing through a gap or over an edge
  • Intensity is a measure of power delivered per unit area, affected by slit width
• Refraction:

  • Refraction occurs when a wave changes speed crossing into a new medium
  • Refractive index measures how much light slows down in a material
  • Snell's Law calculates refractive index from angles of incidence and refraction
• Total Internal Reflection:

  • Light entering a less dense material refracts away from the normal
  • Critical angle is the angle for total internal reflection to occur
  • Optical fibres use total internal reflection to transfer signals
• Optical Fibres:

  • Step-index optical fibres consist of a core and cladding with different refractive indexes
  • Cladding provides tensile strength, prevents information transfer between cores, and protects the core from damage
• Absorption:

  • Absorption results in energy loss as the signal is transferred through optical fibre
  • Absorption can be reduced by using optical fibre repeaters to boost the signal
• Dispersion:

  • Modal dispersion results from beams entering the fibre at different angles, causing pulse broadening
  • Material dispersion is due to different wavelengths traveling at different speeds, also causing pulse broadening
• Amplitude: Maximum displacement of a vibrating particle
• • Wavelength: Shortest distance between two particles in phase
• Frequency: Number of wave cycles occurring each second
• Wave speed: Distance travelled by a wave each second
• Phase difference: Measured in degrees or radians, the amount by which one wave lags behind another wave
• Progressive waves: Waves whose oscillations travel and transfer energy
• Coherent Source Conditions:

  • Same frequency
  • Constant Phase Difference
• • microwaves are transverse, sound are longitudinal
  • microwaves can be polarised but sound can't
  • microwaves have a higher frequency than sound

  
• • constant phase difference
  • same frequency

  
• • microwaves are polarised

  
• • Rotate the aerial in the vertical plane
  • When aerial vertical signal is a maximum
  • Max. occurs when aerial aligned with the plane of polarisation of microwave

  
• • Recieved signal goes through series of max and min
  • Reflected and deflected microwaves interfere
  • Path length of reflected wave increases as plate moved
  • Phase difference between reflected and deflected waves changes so signal strength changes

  
• • Equation is only valid if the slit screen distance is a lot greater than slit separation

  
• • Light bends away from the normal when it speeds up

  
• Fast

  Away (from the normal)

  Slow

  Towards (the normal)
• • internal ray travels along a normal

  
• Explain why the ray emerges parallel to the incident ray [2]

  • Each angle of incidence is 45 degrees and TIR occurs
  • It is travelling along the normal in the porro prism
• Discuss whether either of the two suggestions would work [4]

  Using the prism in Figure 9 does not work because:

  • Light would not leave the prism at the original angle
  • Light will escape from the second reflection

  A smaller n does not work because:

  • Larger critical angle
  • which would reduce the value of θ