5. Waves & Particle Nature of Light

• Definitions:

  • Amplitude: A wave’s maximum displacement from the equilibrium position
  • Frequency (f): The number of complete oscillations passing through a point per second
  • Period (T): The time taken for one full oscillation
  • Speed (v): The distance travelled by the wave per unit time
  • Wavelength (λ): The length of one whole oscillation (e.g. the distance between successive peaks/troughs)
• Wave equation:

  • The speed (v) of a wave is equal to the wave’s frequency multiplied by its wavelength
  • λv = f
• Longitudinal waves:

  • In longitudinal waves, the oscillation of particles is parallel to the direction of energy transfer
  • Made up of compressions and rarefactions and can’t travel in a vacuum
• Transverse waves:

  • In transverse waves, the oscillations of particles (or fields)are perpendicular to the direction of energy transfer
  • All electromagnetic (EM) waves are transverse and travel at 3 x 10^8 ms^-1 in a vacuum
• Graphs of transverse and longitudinal waves:

  • Displacement-distance graphs show how the displacement of a particle varies with the distance of wave travel and can be used to measure wavelength
  • Displacement-time graphs show how the displacement of a particle varies with time and can be used to measure the period of a wave
• Further definitions:

  • Phase: The position of a certain point on a wave cycle
  • Phase difference: How much a particle/wave lags behind another particle/wave
  • Path difference: The difference in the distance travelled by two waves
  • Superposition: Where the displacements of two waves are combined as they pass each other
  • Coherence: A coherent light source has the same frequency and wavelength and a fixed phase difference
  • Wavefront: A surface representing points of a wave with the same phase
• Interference:

  • Constructive interference occurs when two waves are in phase and their displacements are added
  • Destructive interference occurs when waves are completely out of phase and their displacements are subtracted
• Phase difference and path difference:

  • Two waves are in phase if they have the same frequency and wavelength and their phase difference is an integer multiple of 360° (2π radians)
  • Two waves are completely out of phase if they have the same frequency and wavelength and their phase difference is an odd integer multiple of 180° (π radians)
• Stationary waves:

  • Formed from the superposition of 2 progressive waves travelling in opposite directions with the same frequency, wavelength, and amplitude
  • No energy is transferred by a stationary wave
  • In phase - constructive interference occurs forming antinodes
  • Completely out of phase - destructive interference occurs forming nodes
• Speed of a transverse wave on a string:

  • Speed (v) = √(T/μ) where T is the tension in the string and μ is the mass per unit length of the string
• Intensity of radiation:

  • Intensity is the power per unit area and can be calculated using I = P/A where P is power and A is the area
• Refractive index and Snell’s law:

  • Refractive index (n) measures how much light slows down passing through a material
  • n = c/v where c is the speed of light in a vacuum and v is the speed of light in the substance
  • Refraction occurs when a wave enters a different medium, causing it to change direction
  • Snell’s law: sinθ1/n1 = sinθ2/n2
• Critical angle:

  • The critical angle (C) is reached when the angle of refraction is exactly 90° and light is refracted along the boundary
• Total internal reflection:

  • Total internal reflection occurs when the angle of incidence is greater than the critical angle and the incident refractive index is greater than the material's refractive index at the boundary
• The power of a lens is measured by finding the reciprocal of the focal length:

  • Power = 1 / focal length
  • Power is positive in converging lenses and negative in diverging lenses
• For thin lenses used in combination, the power of the combination is the sum of the powers of the individual lenses:

  • Power of combination = Power1 + Power2 + ...
• A real image can be projected onto a screen, while a virtual image cannot be projected onto a screen
• The magnification of a lens is the ratio of the size of the image to the size of the object:

  Magnification = image height / object height = u / v

  
  

  Where u is the distance between the object and the lens axis, v is the distance between the lens axis and the image, and f is the focal length
• A polarised wave oscillates in only one plane, and only transverse waves can be polarised
• Diffraction is the spreading out of waves when they pass through or around a gap
• The diffraction grating equation is:

  sin θ = nλ / d

  Where d is the distance between the slits, θ is the angle to the normal, n is the order, and λ is the wavelength
• Electron diffraction experiments show the wave nature of electrons:

  • Electrons interact with small gaps between atoms in a crystal lattice and form an interference pattern on a screen
• De Broglie hypothesis states that all particles have a wave nature and a particle nature
• De Broglie wavelength (λ) can be found using the equation: λ = ph, where h is the Planck constant and p is the momentum of the particle
• Pulse-echo technique is used with ultrasound waves for imaging objects, relies on waves being reflected at boundaries between different materials
• In the photon model of electromagnetic radiation, EM waves travel in discrete packets called photons, with energy directly proportional to their frequency (E = hf)
• Photon energy is directly proportional to frequency, described by the equation: E = hf
• Threshold frequency is the minimum frequency of light required to emit photoelectrons, work function is the minimum energy required for electrons to be emitted from the surface of a metal
• Photoelectric equation shows the relationship between work function, frequency of light, and maximum kinetic energy of emitted photoelectrons: hf = Φ + KE(max)
• Electronvolt (eV) is a unit of energy, used to express small energies, where 1 eV is equal to the kinetic energy of an electron accelerated across a potential difference of 1 V or 1.6 x 10^-19 J
• Photoelectric effect demonstrates evidence for the particle nature of electromagnetic radiation
• Atomic line spectra show that electrons in atoms can only exist in discrete energy levels, and transitions between these levels result in the emission or absorption of photons
• Energy difference between two energy levels is equal to a specific photon energy emitted or absorbed, calculated using the formula: EΔ = E1 - E2
• Photon frequency can be found using the equation: f = (E1 - E2) / h, where f is the photon frequency and h is the Planck constant