Waves and Particle Nature of Light

Longitudinal waves

Waves where the oscillation of particles is parallel to the direction of energy transfer, made up of compressions and rarefactions.

Transverse waves

Waves where the oscillations of particles (or fields) are at right angles to the direction of energy transfer.

Standing wave

Formed from the superposition of 2 progressive waves, travelling in opposite directions in the same plane, with the same frequency, wavelength, and amplitude.

Superposition

Where the displacements of two waves are combined as they pass each other, resulting in the vector sum of each wave's displacement.

Constructive interference

Occurs when two waves are in phase and so their displacements are added.

Stationary waves

Formed from the superposition of 2 progressive waves, travelling in opposite directions in the same plane, with the same frequency, wavelength, and amplitude, where no energy is transferred.

Speed of a transverse wave on a string

Calculated using the formula v = √(T/μ), where v is the speed, T is the tension in the string, and μ is the mass per unit length of the string.

Snell's law

Used for calculations involving the refraction of light, expressed as sinθ1/n1 = sinθ2/n2, where n1 is the refractive index of material 1, n2 is the refractive index of material 2, θ1 is the angle of incidence of the ray in material 1, and θ2 is the angle of refraction of the ray in material 2.

Critical angle (C)

The angle of incidence at which the angle of refraction is exactly 90°, calculated using the formula sinC = n2/n1, where n is the refractive index of the material.

Total internal reflection (TIR)

Occurs when the angle of incidence is greater than the critical angle and the incident refractive index is greater than the refractive index of the material at the boundary.

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.

Displacement-distance graphs

Graphs showing how the displacement of a particle varies with the distance of wave travel, used to measure wavelength.

Displacement-time graphs

Graphs showing how the displacement of a particle varies with time, used to measure the period of a wave.

Phase

The position of a certain point on a wave cycle, measured in radians, degrees, or fractions of a cycle.

Phase difference

How much a particle/wave lags behind another particle/wave, measured in radians, degrees, or fractions of a cycle.

Path difference

The difference in the distance travelled by two waves.

Coherence

A coherent light source has the same frequency and wavelength and a fixed phase difference.

Wavefront

A surface used to represent the points of a wave which have the same phase.

Destructive interference

Occurs when the waves are completely out of phase and so their displacements are subtracted.

Phase difference and path difference relation

The phase difference (in radians) of two waves with the same frequency and their path differences are related by Δϕ = (Δx * 2π) / λ.

Intensity

The power (energy transferred per unit time) per unit area, calculated using the equation I = P/A, where P is the power and A is the area.

Refractive index (n)

A property of a material which measures how much it slows down light passing through it, calculated by dividing the speed of light in a vacuum by the speed of light in that substance.

Pulse-echo technique

Used with ultrasound waves for the imagining of objects, relying on the fact that waves are reflected when they meet boundaries between different materials.

Photon energy

Directly proportional to the frequency of the photon, expressed as E = hf, where E is the photon energy, h is Planck's constant, and f is the wave frequency.

Electronvolt (eV)

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.

Atomic line spectra

Discrete values of wavelength emitted by a fluorescent tube, providing evidence that electrons in atoms can only transition between discrete energy levels.

de Broglie relation

Hypothesis stating that all particles have a wave nature and a particle nature, with the wavelength of any particle found using the equation λ = h/p, where λ is the de Broglie wavelength, h is the Planck constant, and p is the momentum of the particle.

Wave behaviour at an interface

Waves can be transmitted or reflected at an interface, with transmitted waves passing into the next material and reflected waves bouncing off the interface without passing into the next material.

Diffraction grating equation

Used to find the angle to the normal made by the maximum (light fringe) when light is passed through a diffraction grating, expressed as sinθ/λ = d/n, where d is the distance between the slits, θ is the angle to the normal, n is the order, and λ is the wavelength.

Photoelectric effect

Where photoelectrons are emitted from the surface of a metal after light above a certain frequency is shone on it, providing evidence for the particle nature of EM radiation.

Threshold frequency

The minimum frequency of light required to emit photoelectrons, varying depending on the type of metal.

Work function

The minimum energy required for electrons to be emitted from the surface of a metal.

Electronvolt (eV)

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.

Atomic line spectra

Discrete values of wavelength emitted by a fluorescent tube, providing evidence that electrons in atoms can only transition between discrete energy levels.

Wave behaviour at an interface

Waves can be transmitted or reflected at an interface, with transmitted waves passing into the next material and reflected waves bouncing off the interface without passing into the next material.

Diffraction grating equation

Used to find the angle to the normal made by the maximum (light fringe) when light is passed through a diffraction grating, expressed as sinθ/λ = d/n, where d is the distance between the slits, θ is the angle to the normal, n is the order, and λ is the wavelength.

Photoelectric effect

Where photoelectrons are emitted from the surface of a metal after light above a certain frequency is shone on it, providing evidence for the particle nature of EM radiation.

Threshold frequency

The minimum frequency of light required to emit photoelectrons, varying depending on the type of metal.

Work function

The minimum energy required for electrons to be emitted from the surface of a metal.

Photoelectric equation

Shows the relationship between the work function, the frequency of light, and the maximum kinetic energy of the emitted photoelectrons, expressed as E = hf = Φ + Ek(max), where E is the photon energy, Φ is the work function, and Ek(max) is the maximum kinetic energy.

Electronvolt (eV)

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.

Atomic line spectra

Discrete values of wavelength emitted by a fluorescent tube, providing evidence that electrons in atoms can only transition between discrete energy levels.

Wave behaviour at an interface

Waves can be transmitted or reflected at an interface, with transmitted waves passing into the next material and reflected waves bouncing off the interface without passing into the next material.

Diffraction grating equation

Used to find the angle to the normal made by the maximum (light fringe) when light is passed through a diffraction grating, expressed as sinθ/λ = d/n, where d is the distance between the slits, θ is the angle to the normal, n is the order, and λ is the wavelength.

Photoelectric effect

Where photoelectrons are emitted from the surface of a metal after light above a certain frequency is shone on it, providing evidence for the particle nature of EM radiation.

Threshold frequency

The minimum frequency of light required to emit photoelectrons, varying depending on the type of metal.

Work function

The minimum energy required for electrons to be emitted from the surface of a metal.

Photoelectric equation

Shows the relationship between the work function, the frequency of light, and the maximum kinetic energy of the emitted photoelectrons, expressed as E = hf = Φ + Ek(max), where E is the photon energy, Φ is the work function, and Ek(max) is the maximum kinetic energy.

Electronvolt (eV)

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.

Atomic line spectra

Discrete values of wavelength emitted by a fluorescent tube, providing evidence that electrons in atoms can only transition between discrete energy levels.

Wave behaviour at an interface

Waves can be transmitted or reflected at an interface, with transmitted waves passing into the next material and reflected waves bouncing off the interface without passing into the next material.

Diffraction grating equation

Used to find the angle to the normal made by the maximum (light fringe) when light is passed through a diffraction grating, expressed as sinθ/λ = d/n, where d is the distance between the slits, θ is the angle to the normal, n is the order, and λ is the wavelength.

Photoelectric effect

Where photoelectrons are emitted from the surface of a metal after light above a certain frequency is shone on it, providing evidence for the particle nature of EM radiation.

Threshold frequency

The minimum frequency of light required to emit photoelectrons, varying depending on the type of metal.

Work function

The minimum energy required for electrons to be emitted from the surface of a metal.

Photoelectric equation

Shows the relationship between the work function, the frequency of light, and the maximum kinetic energy of the emitted photoelectrons, expressed as E = hf = Φ + Ek(max), where E is the photon energy, Φ is the work function, and Ek(max) is the maximum kinetic energy.

Electronvolt (eV)

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.

Atomic line spectra

Discrete values of wavelength emitted by a fluorescent tube, providing evidence that electrons in atoms can only transition between discrete energy levels.

Wave behaviour at an interface

Waves can be transmitted or reflected at an interface, with transmitted waves passing into the next material and reflected waves bouncing off the interface without passing into the next material.

Diffraction grating equation

Used to find the angle to the normal made by the maximum (light fringe) when light is passed through a diffraction grating, expressed as sinθ/λ = d/n, where d is the distance between the slits, θ is the angle to the normal, n is the order, and λ is the wavelength.

Photoelectric effect

Where photoelectrons are emitted from the surface of a metal after light above a certain frequency is shone on it, providing evidence for the particle nature of EM radiation.

Threshold frequency

The minimum frequency of light required to emit photoelectrons, varying depending on the type of metal.

Work function

The minimum energy required for electrons to be emitted from the surface of a metal.

Photoelectric equation

Shows the relationship between the work function, the frequency of light, and the maximum kinetic energy of the emitted photoelectrons, expressed as E = hf = Φ + Ek(max), where E is the photon energy, Φ is the work function, and Ek(max) is the maximum kinetic energy.

Electronvolt (eV)

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.

Atomic line spectra

Discrete values of wavelength emitted by a fluorescent tube, providing evidence that electrons in atoms can only transition between discrete energy levels.

Wave behaviour at an interface

Waves can be transmitted or reflected at an interface, with transmitted waves passing into the next material and reflected waves bouncing off the interface without passing into the next material.

Diffraction grating equation

Used to find the angle to the normal made by the maximum (light fringe) when light is passed through a diffraction grating, expressed as sinθ/λ = d/n, where d is the distance between the slits, θ is the angle to the normal, n is the order, and λ is the wavelength.

Photoelectric effect

Where photoelectrons are emitted from the surface of a metal after light above a certain frequency is shone on it, providing evidence for the particle nature of EM radiation.

Threshold frequency

The minimum frequency of light required to emit photoelectrons, varying depending on the type of metal.

Work function

The minimum energy required for electrons to be emitted from the surface of a metal.