## Wave

A wave is a disturbance that travels through a medium or space, transporting energy from one point to another. Waves can travel through a medium, like waves rippling across a lake, or through space, like the electromagnetic waves that carry sunlight to Earth.

• All waves have shared characteristics such as height (amplitude), peaks (crests), direction of movement, rate of oscillation (frequency), and distance between peaks (wavelength).
• The speed of a wave depends on the medium it travels through. For example, sound waves travel slower through air than through water. In contrast, electromagnetic waves travel at a constant speed (the speed of light) in a vacuum.
• Electromagnetic waves are generally invisible to the human eye, except for the visible spectrum, with wavelengths between approximately 400 and 700 nanometres.
• Beyond this range, whether the wavelengths are longer (as in radio and microwaves) or shorter (as in ultraviolet, X-rays, and gamma rays), our eyes cannot detect them.
• Although we cannot see most electromagnetic waves, we can perceive some of them in other ways. For instance, infrared waves are felt as heat, and electric current (which produces electromagnetic waves) can cause a buzzing sensation in a wire or cause electrocution.
##### Wavelength & frequency
• The wavelength of electromagnetic waves can vary greatly, from extremely long radio waves, sometimes measured in kilometres, to very short gamma rays, measured in picometers (there are a trillion picometers in a metre (10^12)).
• The frequency of electromagnetic waves can also range from extremely low (1 cycle per second, known as 1 hertz) to extremely high, such as a quadrillion cycles per second, which equals 10^15 hertz (10^15).
• When you throw a stone into a pond, it creates a series of ripples, or waves, that propagate outward in concentric circles until they encounter obstacles.
• Out in the world, waves are generated when forces such as wind and tide disturb the water’s surface.
• The wavelength of a wave in water can be determined by measuring the distance from the crest of one wave to the crest of the next wave.
• The frequency of waves in water can be determined by counting the number of waves that reach their peak or crest at a specific point over a set period of time.
• The amplitude of a wave is often approximated by measuring half the vertical distance from the top of a wave (the crest) to the bottom of a wave (the trough). However, strictly speaking, it should be the distance from the undisturbed surface level of the water to the next crest or trough. This is an approximation because it assumes that waves are symmetrical and that the undisturbed water level is midway between the crest and the trough.
• The direction of travel of water waves can typically be easily determined by observing their movement.
• The energy carried by waves at the beach becomes evident when you experience their force while swimming, for instance, being toppled over by a wave.
• A wave is a disturbance that travels through a medium or space, transporting energy from one point to another. Waves can travel through a medium, like waves rippling across a lake, or through space, like the electromagnetic waves that carry sunlight to Earth.
• Electromagnetic waves are generally invisible to the human eye, except for the visible spectrum, with wavelengths between approximately 400 and 700 nanometres.
• Beyond this range, whether the wavelengths are longer (as in radio and microwaves) or shorter (as in ultraviolet, X-rays, and gamma rays), our eyes cannot detect them.
• Although we cannot see most electromagnetic waves, we can perceive some of them in other ways. For instance, infrared waves are felt as heat, and electric current (which produces electromagnetic waves) can cause a buzzing sensation in a wire or cause electrocution.

## Wave diagram

A wave diagram is a graphic representation, using specific drawing rules and labels, that depicts variations in the characteristics of light waves. These characteristics include changes in wavelength, frequency, amplitude, speed of light and propagation direction.

• A wave diagram provides a visual representation of how a wave behaves when it interacts with various different media or objects.
• The purpose of a wave diagram is to illustrate optical phenomena, including reflection, refraction, dispersion, and diffraction.
• Wave diagrams can be useful in both theoretical and practical applications, such as understanding the basics of the physics of light  or when designing complex optical systems.
• Wave diagrams are not limited to light; they can also be used to represent other types of waves, such as sound or radio waves.
• A wave diagram is a graphic representation, using specific drawing rules and labels, that depicts variations in the characteristics of light waves. These characteristics include changes in wavelength, frequency, amplitude, speed of light and propagation direction.
• A wave diagram provides a visual representation of how a wave behaves when it interacts with various different media or objects.
• The purpose of a wave diagram is to illustrate optical phenomena, including reflection, refraction, dispersion, and diffraction.
• Wave diagrams can be useful in both theoretical and practical applications, such as understanding the basics of the physics of light  or when designing complex optical systems.

## Wave diagram conventions

• Absorption: Absorption is the process by which a material absorbs some or all of the energy of light. This can be represented by a decrease in the amplitude of the wave as it passes through the material.
• Brewster’s angle: Brewster’s angle is the angle of incidence at which light is polarized when it reflects off a surface. This can be represented by a line or an arrow indicating the direction of polarization of the reflected light.
• Diffraction: Diffraction is the bending of waves around obstacles or through narrow openings. Diffraction can cause waves to spread out and interfere with each other.
• Dispersion: Dispersion is the phenomenon where the speed of light varies with its frequency or wavelength. This can be represented by a graph showing the variation of the refractive index with wavelength or frequency.
• Frequency: Frequency is the number of wave cycles that occur in one second. It is typically represented by the symbol f and is measured in Hertz (Hz).
• Huygens-Fresnel principle: The Huygens-Fresnel principle states that every point on a wavefront can be considered as the source of secondary spherical waves, and the sum of these waves determines the shape of the wavefront at a later time. This can be represented by drawing small circles around each point on a wavefront to represent the secondary waves.
• Interference: Interference is the interaction of two or more waves that meet at the same point in space and time. Interference can be constructive, where the amplitudes of the waves add up, or destructive, where the amplitudes of the waves cancel each other out.
• Phase: Phase is a measure of the position of a wave relative to a reference point in time. It is typically represented by the symbol ϕ and is measured in radians.
• Period: Period is the time it takes for one wave cycle to occur. It is the reciprocal of frequency and is typically represented by the symbol T and is measured in seconds.
• Phase velocity and group velocity: Phase velocity is the speed at which the wavefronts propagate, while group velocity is the speed at which the wave packet (a group of waves with slightly different frequencies) propagates. These can be represented by arrows showing the direction and speed of the wavefronts and wave packet.
• Polarization: Polarization is the orientation of the electric field of a wave in a particular direction. Polarization can be linear, circular, or elliptical. It is typically represented by an arrow or a symbol.
• Polarization plane: The polarization plane is the plane in which the electric field vector of a polarized light wave vibrates. This can be represented by a line or an arrow indicating the direction of the electric field vector.
• Reflection: Reflection is the bouncing back of a wave after it strikes a boundary between two media. This can be represented by the wavefronts reflecting off the boundary and changing direction.
• Refraction: Refraction is the bending of a wave as it passes from one medium to another with a different refractive index. This can be represented by a change in the direction of the wavefronts at the boundary between the two media.
• Scattering: Scattering is the process by which light is redirected in many directions as it passes through a medium with irregularities or particles. This can be represented by arrows indicating the directions in which the scattered light is going.
• Snell’s law: Snell’s law relates the angle of incidence and refraction of light at the boundary between two media with different refractive indices. This can be represented by a diagram showing the path of the incident and refracted rays and the angles of incidence and refraction.
• Standing waves: Standing waves are patterns that result from the interference of two waves of the same frequency travelling in opposite directions. They have nodes, where the amplitude of the wave is zero, and antinodes, where the amplitude is at a maximum. These can be represented by dashed lines or nodes and antinodes marked on a wave diagram.
• Wavefronts: Wavefronts are imaginary surfaces that represent the points of a wave that are in phase with each other. In a two-dimensional diagram, wavefronts are represented by lines that are perpendicular to the direction of wave propagation.
• Wavelength: Wavelength is the distance between two successive wavefronts of a wave. It is typically represented by the symbol λ and is measured in meter.
• Wavevector: Wavevector is a vector that represents the direction of wave propagation and the wavelength of the wave. It is typically represented by the symbol k and is measured in reciprocal meters (m⁻¹).

## Wave function

In Quantum Mechanics, a wave function is a mathematical function that describes the quantum state of a physical system, such as a particle or a collection of particles.

• A wave function provides information about the probabilities of various possible states the system might be in. It depends on the coordinates of the particles in the system (for example, position or momentum). It calculates the probability of finding the system in a particular state.
• Wave functions are used to determine the probability of various outcomes in quantum experiments.
• A wave function, in the context of quantum mechanics, must encapsulate a wealth of information about a quantum system, including its possible states, probabilities, and how it evolves over time:
• Position and Momentum: The wave function must provide information about the possible positions and momenta of particles within the system. This information is crucial for predicting the outcomes of measurements.
• Superposition: It should be able to represent the idea that a quantum system can exist in a superposition of multiple possible states. This means that the system can simultaneously occupy different states with certain probabilities until observed.
• Probability Amplitudes: The wave function encodes probability amplitudes, which are complex numbers that determine the likelihood of finding the system in a particular state upon measurement.
• Time Evolution: It should be able to evolve over time, allowing for the prediction of how the system’s state will change over the course of time.
• Observable Properties: The wave function must account for the possible values of observable properties (such as energy, angular momentum, etc.) and their corresponding probabilities.
• Normalization: It must satisfy the condition of normalization, meaning that the total probability of finding the system in any possible state must equal 1.
• Boundary Conditions: For specific physical systems, the wave function must satisfy appropriate boundary conditions that reflect the constraints imposed on the system (e.g., within a finite box or in a specific potential field).
• Interference and Entanglement: It should be capable of describing interference effects between different states and, in the case of multiple particles, account for entanglement, where the states of particles become correlated.
• Wave Function Collapse: When a measurement is made, the wave function must be capable of undergoing a transition from a superposition of states to a single, definite state, in accordance with the process of wave function collapse.
• Completeness and Orthogonality: In certain mathematical formulations of quantum mechanics, wave functions must form a complete and orthogonal set to be used as a basis for representing quantum states.
##### Wave Function Collapse

Wave function collapse is a phenomenon in quantum mechanics where the act of making a measurement on a quantum system causes it to transition from a superposition of multiple possible states to a single, definite state.

• Prior to measurement, a quantum system can exist in a superposition of states, meaning it simultaneously occupies multiple possible states with different probabilities – these are described by the wave. However, when a measurement is made, the wave function collapses, and the system assumes one of the possible states with certainty.
• Wave function collapse illustrates the profound influence that observation has on the behaviour of quantum systems.
• In the context of quantum mechanics, “observation” refers to the act of making a measurement or carrying out an experiment to gain information about a quantum system. When we observe a quantum system, we are attempting to determine one of its properties, such as position, momentum, energy, etc.
• The interpretation of wave function collapse is a subject of ongoing debate among physicists, with various interpretations positing different explanations for the phenomenon.
###### References
• In Quantum Mechanics, a wave function is a mathematical function that describes the quantum state of a physical system, such as a particle or a collection of particles.
• A wave function provides information about the probabilities of various possible states the system might be in. It depends on the coordinates of the particles in the system (for example, position or momentum). It calculates the probability of finding the system in a particular state.
• Wave functions are used to determine the probability of various outcomes in quantum experiments.
• A wave function, in the context of quantum mechanics, must encapsulate a wealth of information about a quantum system, including its possible states, probabilities, and how it evolves over time:

## Wave-cycle

A wave cycle is the complete up-and-down motion of a wave, from one crest (peak) to the next crest, or from one trough (dip) to the next trough. Visualize a wave cycle as a series of points plotted along the path of a wave from one crest to the subsequent crest.

• All electromagnetic waves have common characteristics like crests, troughs, vibrations, wavelength, frequency, amplitude, and propagation direction.
• As a wave vibrates, a wave cycle can be seen as a sequence of individual vibrations, measured from one peak to the next, one trough to the next, or from the start of one wave cycle to the start of the next.
• While a wave cycle refers to the path from one point on a wave during a single oscillation to the same point on completion of that oscillation, wavelength is a measurement of the same phenomenon but in a straight line along the axis of the wave.
• Wavelength refers specifically to the horizontal distance between equivalent points in a single wave cycle, such as the distance between two consecutive crests or troughs.
• In contrast, a wave cycle encompasses the entire up-and-down movement of the wave, including the horizontal distance (wavelength) and the vertical displacement.
###### References
• A wave cycle is the complete up-and-down motion of a wave, from one crest (peak) to the next crest, or from one trough (dip) to the next trough. Visualize a wave cycle as a series of points plotted along the path of a wave from one crest to the subsequent crest.
• All electromagnetic waves have common characteristics like crests, troughs, vibrations, wavelength, frequency, amplitude, and propagation direction.
• As a wave vibrates, a wave cycle can be seen as a sequence of individual vibrations, measured from one peak to the next, one trough to the next, or from the start of one wave cycle to the start of the next.
• While a wave cycle refers to the path from one point on a wave during a single oscillation to the same point on completion of that oscillation, wavelength is a measurement of the same phenomenon but in a straight line along the axis of the wave.

## Wave-cycle

A wave-cycle refers to the path of a wave measured from any point through the course of a single oscillation to the same point on the next oscillation.

• Imagine a wave-cycle as a series of points marked on the path of the wave between one crest and the next.
• All electromagnetic waves share features such as crests, troughs, oscillations, wavelength, frequency, amplitude, direction of travel.
• Whilst a wave-cycle is the path from one point on a wave during a single oscillation to the same point on completion of that oscillation, wavelength is a measurement of the same phenomenon along the axis of the wave.

## Wave-fronts, diffraction & interference

###### Wavefronts

Parallel electromagnetic waves with a common point of origin, the same frequency and phase, and propagating through the same medium, produce an advancing wavefront perpendicular to their direction of travel.

Point sources emitting electromagnetic waves in all directions, at same frequency and phase, and propagating through the same medium, produce spherical wavefronts tangental to their origin.

• Diffraction describes the way light waves bend around the edges of an obstacle into regions that would otherwise be in shadow.
• An object or aperture that causes diffraction is treated as being the location of a secondary source of wave propagation.
• Diffraction causes a propagating wave to produce a distinctive pattern when it subsequently strikes a surface.
• Diffraction produces a circular pattern of concentric bands when a narrow beam of light passes through a small circular aperture.
• In classical physics, the diffraction of electromagnetic waves is described by treating each point in a propagating wavefront as an individual spherical wavelet.
• As each wavelet encounters the edge of an obstacle it bends independently of every other. However, interference between wavelets alters the angle to which they bend and the distance they must travel before striking a surface.
• The explanations that best describe the process of diffraction belong to Wave Theory and are the result of two centuries of study in the field of optics.
• In modern quantum mechanics, diffusion is explained by referring to the wave function and probability distribution of each photon of light when it encounters the corner of an obstacle or the edge of an aperture.
• A wave function is a mathematical description concerning the probable distribution of outcomes of every possible measurement of a photon’s behaviour.

## Wave-particle duality

Wave-particle duality is a fundamental concept in quantum mechanics that describes the dual nature of particles, which can exhibit both wave-like and particle-like behaviour.

• Wave-particle duality refers to the phenomenon where entities like light can exhibit characteristics of both waves and particles.
•  Electromagnetic radiation, including light, is often described using wave properties. However, when it interacts with matter, it behaves like particles.
•  A photon is a quantum of electromagnetic radiation and represents the smallest discrete amount of light energy.
• When a photon is absorbed by matter, the energy becomes localized at specific points. This phenomenon is termed ‘wave function collapse.’ It describes the transition of a quantum system from a superposition of states to a definite state upon measurement.
• Wave-particle duality is a fundamental aspect of quantum mechanics and applies to all particles, not just light. Particles like electrons also exhibit wave-like and particle-like behaviour.
• The double-slit experiment is an experiment in quantum physics that demonstrates the wave-like behaviour of particles, including photons and electrons, and is a key illustration of wave-particle duality.

Concepts used to describe light as waves and particles can be paired to illustrate the wave-particle character of light

##### Explanation
FrequencyEnergyFrequency is related to the energy of a photon. Higher frequency light corresponds to higher energy photons. This is described by Planck's equation E = hf, where E is energy, h is Planck's constant, and f is frequency.
WavelengthMomentumThe wavelength of a wave is inversely proportional to its momentum. This is described by the de Broglie wavelength formula λ = h/p, where λ is wavelength, h is Planck's constant, and p is momentum.
Wave speedMomentumThe speed of a wave is related to its momentum through its frequency and wavelength. For light, the speed of propagation (c, the speed of light) is equal to its frequency times wavelength (c = λf), which is also related to its momentum as described above.
AmplitudeIntensityThe amplitude of a wave determines its intensity, which is related to the brightness or energy density of light. Higher amplitude corresponds to higher intensity.
PeriodLifetimeThe period of a wave is the time it takes for one complete cycle. In the context of light particles (photons), their "lifetime" refers to the duration of their existence before they are absorbed or undergo a different process.
PhaseQuantum statePhase refers to the position of a point in a wave cycle, and it can be related to the quantum state of a particle. In quantum mechanics, a particle's state is described by a complex-valued wavefunction, and the phase of this wavefunction is significant in determining probabilities and interference patterns.

These pairings are all based on the wave-particle duality of matter, which states that all objects have both wave-like and particle-like properties.

The specific pairings in the table can be derived from the following equations:

• E = hf (Planck’s equation describes the relationship between the energy of a photon and its frequency.)
• p = h/λ (de Broglie wavelength equation describes the relationship between the momentum of a particle and its wavelength.)
• p = mv (momentum equation describes the relationship between the momentum of a particle and its mass and velocity.)
• I = 1/2 cε_0 E^2 (intensity equation describes the relationship between the intensity of an electromagnetic wave and its electric field.)

where:

• E is energy
• f is frequency
• p is momentum
• m is mass
• v is velocity
• λ is wavelength
• I is intensity
• c is the speed of light
• ε_0 is the permittivity of free space. The permittivity of free space, also known as the electric constant, is a fundamental constant of nature. It is a measure of how easily an electric field can penetrate a vacuum.

The equation E = hf tells us that the energy of a particle is proportional to its frequency. This means that the higher the frequency of a particle, the more energy it has. This is why high-frequency radiation, such as gamma rays and X-rays, is so dangerous.

The equation p = h/λ tells us that the momentum of a particle is inversely proportional to its wavelength. This means that the shorter the wavelength of a particle, the more momentum it has. This is why high-energy particles, such as protons and electrons, can be used to accelerate other particles to high speeds.

• Wave-particle duality is a fundamental concept in quantum mechanics that describes the dual nature of particles, which can exhibit both wave-like and particle-like behaviour.
• Wave-particle duality refers to the phenomenon where entities like light can exhibit characteristics of both waves and particles.
•  Electromagnetic radiation, including light, is often described using wave properties. However, when it interacts with matter, it behaves like particles.
•  A photon is a quantum of electromagnetic radiation and represents the smallest discrete amount of light energy.
• When a photon is absorbed by matter, the energy becomes localized at specific points. This phenomenon is termed ‘wave function collapse.’ It describes the transition of a quantum system from a superposition of states to a definite state upon measurement.
• Wave-particle duality is a fundamental aspect of quantum mechanics and applies to all particles, not just light. Particles like electrons also exhibit wave-like and particle-like behaviour.

## Wavefront

Electromagnetic waves that are parallel, share a common starting point, have the same frequency and phase, and move through the same medium, form an advancing wavefront at right angles to their direction of travel.

• A wavefront is a conceptual tool used in the study of waves, including electromagnetic waves like light. It refers to the locus of all points that are in phase with each other along the wave at a given instant. In other words, it represents the leading edge of a wave as it propagates through a medium.
• Sources that emit light in all directions, known as point sources, generate spherical wavefronts.
• Lasers, which produce a narrow beam of parallel rays, create waves with flat wavefronts.
• An electromagnetic wave with a flat wavefront is known as a plane wave.
• In addition to plane waves and spherical waves, there are also cylindrical waves which are produced when a point source is extended along a straight line.
• The shape of the wavefront can be influenced by interaction with different mediums or obstacles, such as when:
• Refraction causes the path of light to bend as it crosses the boundary between two transparent media.
• Dispersion causes light to separate into its constituent wavelengths, each of which bends to a different degree as it crosses the boundary between two transparent media.
• Diffraction causes light to bend around the edges of obstacles into regions that would otherwise be in shadow.
• The concept of wavefronts applies not only to light but also to other types of waves such as sound waves or water waves.
• Wavefronts are typically used to describe the behaviour of waves in classical physics, where waves exhibit properties such as interference, diffraction, and refraction.
• While wavefronts are often associated with the behaviour of light, which can exhibit both wave-like and particle-like properties, they are a description of the wave nature of light rather than individual photons.
• At the quantum level, the behaviour of individual photons is described differently, often using concepts such as wave functions in quantum mechanics.
###### References
• Electromagnetic waves that are parallel, share a common starting point, have the same frequency and phase, and move through the same medium, form an advancing wavefront at right angles to their direction of travel.
• A wavefront is a conceptual tool used in the study of waves, including electromagnetic waves like light. It refers to the locus of all points that are in phase with each other along the wave at a given instant. In other words, it represents the leading edge of a wave as it propagates through a medium.
• Sources that emit light in all directions, known as point sources, generate spherical wavefronts.
• Lasers, which produce a narrow beam of parallel rays, create waves with flat wavefronts.
• An electromagnetic wave with a flat wavefront is known as a plane wave.
• In addition to plane waves and spherical waves, there are also cylindrical waves which are produced when a point source is extended along a straight line.

## Wavelength

Wavelength is a measurement from any point on the path of a wave to the same point on its next oscillation. The measurement is made parallel to the centre-line of the wave.

## Wavelength

Wavelength is the distance from any point on a wave to the corresponding point on the next wave. This measurement is taken along the middle line of the wave.

• While wavelength can be measured from any point on a wave, it is often simplest to measure from the peak of one wave to the peak of the next, or from the bottom of one trough to the bottom of the next, ensuring the measurement covers a whole wave cycle.
• The wavelength of an electromagnetic wave is usually given in metres.
• The wavelength of visible light is typically measured in nanometres, with 1,000,000,000 nanometres making up a metre.
• Each type of electromagnetic radiation – such as radio waves, visible light, and gamma waves – corresponds to a specific range of wavelengths on the electromagnetic spectrum.
• As energy increases, frequency also increases and the wavelength decreases. Therefore, shorter wavelengths correspond to higher energy levels, and longer wavelengths correspond to lower energy levels.
##### Wavelength & the Visible Spectrum
• The visible part of the electromagnetic spectrum consists of a range of wavelengths that correspond with all the different colours we see in the world.
• The visible spectrum, which spans wavelengths from approximately 400 to 700 nanometres, is commonly described in terms of bands of colour—red, orange, yellow, green, blue, indigo, and violet.
• However, these divisions are somewhat arbitrary since the spectrum is continuous, and the exact wavelength boundaries between colours is subjective.
• Humans don’t see the wavelengths of visible light directly but do see the specific colour associated with each wavelength and the colour produced when different wavelengths mix.
• Within this visible spectrum, each colour corresponds to a single wavelength of light.
• The concept of colour is a perceptual property, not a property of light itself.
• It’s how our brain interprets the wavelengths of light that reach our eyes. The perceived colour (hue) of a light stimulus is dependent on its wavelength.
• A colour produced by a single wavelength is known as a pure spectral colour.
##### Wavelength & Colour
• A light that we perceive as white is a combination of many different wavelengths of light across the visible spectrum. When these wavelengths containing red, green, and blue mix and reflect off a neutral-coloured surface, they appear white to our eyes.
• Light sources in nature rarely emit a single wavelength. They typically emit a mixture of many wavelengths that combine to create the colour we perceive upon reflection. The wider the range of wavelengths present in the light source, the less saturated (more diluted) the reflected colour will appear. In other words, light with a mix of many wavelengths tends to appear lighter or closer to white.
• Wavelengths of visible light are typically measured in nanometers (nm). While the human eye cannot distinguish every single possible wavelength within the visible spectrum (between 400 nm and 700 nm), it can differentiate a vast range of colours within that spectrum.
###### References
• Wavelength is the distance from any point on a wave to the corresponding point on the next wave. This measurement is taken along the middle line of the wave.
• While wavelength can be measured from any point on a wave, it is often simplest to measure from the peak of one wave to the peak of the next, or from the bottom of one trough to the bottom of the next, ensuring the measurement covers a whole wave cycle.
• The wavelength of an electromagnetic wave is usually given in metres.
• The wavelength of visible light is typically measured in nanometres, with 1,000,000,000 nanometres making up a metre.
• Each type of electromagnetic radiation – such as radio waves, visible light, and gamma waves – corresponds to a specific range of wavelengths on the electromagnetic spectrum.

## Wavelengths of light & colour vision

###### About wavelengths of light and colour vision

There is a clear difference between the wavelengths of light that make up the visible spectrum and how the human eye converts the information it receives about wavelength into the perception of colour.

• The human eye, and so visual perception, is tuned to the visible spectrum and so to spectral colours between red and violet.
• It is the sensitivity of the eye to this small part of the electromagnetic spectrum that results in the perception of colour.
• Photosensitive cone cells embedded in the retina of each eye respond to wavelengths of light corresponding with spectral colours.
• Explained in simple terms, cone cells distinguish between different colours by determining how much red, green and blue are present when stimulated by their corresponding wavelengths.
• The system used by the human eye to distinguish colours is called trichromacy or trichromatic colour vision.
• The spread of wavelengths that the spectral colour model is concerned with is well suited to a linear arrangement with the shortest at one and the longest at the other.
• The way the human eye determines colour from the presence of three primary colours (red, green and blue) lends itself to a circular, wheel-like arrangement.
• The RGB color model used in digital displays and imaging devices is based on the trichromatic nature of human vision.

## Waves in water

• When you throw a stone into a pond, it creates a series of ripples, or waves, that propagate outward in concentric circles until they encounter obstacles.
• Out in the world, waves are generated when forces such as wind and tide disturb the water’s surface.
• The wavelength of a wave in water can be determined by measuring the distance from the crest of one wave to the crest of the next wave.
• The frequency of waves in water can be determined by counting the number of waves that reach their peak or crest at a specific point over a set period of time.
• The amplitude of a wave is often approximated by measuring half the vertical distance from the top of a wave (the crest) to the bottom of a wave (the trough). However, strictly speaking, it should be the distance from the undisturbed surface level of the water to the next crest or trough. This is an approximation because it assumes that waves are symmetrical and that the undisturbed water level is midway between the crest and the trough.
• The direction of travel of water waves can typically be easily determined by observing their movement.
• The energy carried by waves at the beach becomes evident when you experience their force while swimming, for instance, being toppled over by a wave.

## Weak Nuclear force

The weak nuclear force is one of the four fundamental forces in nature, alongside the electromagnetic force, the strong nuclear force, and gravity. The weak nuclear force played a key role in the creation of elements like hydrogen, helium, and lithium in the early universe. Today, it plays a critical role in the nuclear fusion reactions that power the Sun and other stars.

• The weak nuclear force is responsible for the decay of radioactive isotopes, as well as for other nuclear reactions such as beta decay and neutrino interactions.
• When unstable radioactive isotopes decay, they emit radiation and transform into more stable elements.
• In beta decay, a neutron in the nucleus of an atom decays into a proton, an electron, and an antineutrino. Neutrino interactions occur in nuclear reactors.
• Neutrinos are very light particles that rarely interact with matter, but they can interact with the nuclei of atoms through the weak nuclear force.
• The weak nuclear force is unique compared to other fundamental forces. It’s considered weak because its strength is significantly lower than other forces at the atomic level.
• However, it has a longer range than the strong nuclear force, which acts over very short distances within the nucleus.
• The weak force is also highly selective, specifically interacting only with certain subatomic particles called leptons, which include neutrinos and electrons.
• The weak nuclear force is mediated by a family of particles called W and Z bosons.
###### References
• The weak nuclear force is one of the four fundamental forces in nature, alongside the electromagnetic force, the strong nuclear force, and gravity. The weak nuclear force played a key role in the creation of elements like hydrogen, helium, and lithium in the early universe. Today, it plays a critical role in the nuclear fusion reactions that power the Sun and other stars.The weak nuclear force is responsible for the decay of radioactive isotopes, as well as for other nuclear reactions such as beta decay and neutrino interactions.
• When unstable radioactive isotopes decay, they emit radiation and transform into more stable elements.
• In beta decay, a neutron in the nucleus of an atom decays into a proton, an electron, and an antineutrino. Neutrino interactions occur in nuclear reactors.
• Neutrinos are very light particles that rarely interact with matter, but they can interact with the nuclei of atoms through the weak nuclear force.
• The weak nuclear force is unique compared to other fundamental forces. It’s considered weak because its strength is significantly lower than other forces at the atomic level.
• However, it has a longer range than the strong nuclear force, which acts over very short distances within the nucleus.

## White light

White light is the name given to visible light that contains all wavelengths of the visible spectrum at equal intensities.

• As light travels through a vacuum or a medium it is described as white light if it contains all the wavelengths of visible light.
• As light travels through the air it is invisible to our eyes.
• When we look around we see through the air because it is very transparent and light passes through it.
• The term white light doesn’t mean light is white as it travels through the air.
• One situation in which light becomes visible is when it reflects off the surface of an object.
• When white light strikes a neutral coloured object and all wavelengths are reflected then it appears white to an observer.

## White light

White light is the term for visible light that contains all wavelengths of the visible spectrum at equal intensities.

• The term white light can have two meanings:
• It can refer to a combination of all wavelengths of visible light traveling through space, regardless of observation.
• What a person sees when all colours of the visible spectrum hit a white or neutral-coloured surface.
• The human eye sees white when the wavelengths of light associated with the three primary colours – red, green, and blue (RGB) – are projected onto an achromatic surface.
• White light appears as different colours to an observer when some wavelengths of light are reflected by an object’s surface while others are absorbed. Artificial light sources usually emit light with a varied distribution of wavelengths or intensities, so they don’t typically emit pure white light.
• While there isn’t a single, distinct definition for white light, it’s fair to say that in any given situation:
• White is the lightest possible colour.
• White is an achromatic colour, which means a colour without hue, but with maximum saturation and brightness.
• Colour constancy, the ability to perceive colours as relatively constant, even under changing lighting conditions, enables human observers to see very different whites as appearing the same.
##### Why do Light Bulbs Glow if Light is Invisible?
• Incandescent light bulbs work by passing an electrical current through a thin tungsten filament which has high electrical resistance.
• This resistance causes the filament’s electrons to vibrate and heat up. As the filament gets hot, it emits light.
• The yellowish-white colour we see comes primarily from the heated tungsten surface itself.
• Light bulbs, like most hot objects, also emit wavelengths of light that are outside the visible region of the electromagnetic spectrum.
• These invisible wavelengths are typically infrared radiation, which we feel as heat. Additionally, a small portion of the light emitted might be ultraviolet, but these are blocked by the glass bulb.
###### References
• White light is the term for visible light that contains all wavelengths of the visible spectrum at equal intensities.
• The sun emits white light because sunlight contains all the wavelengths of the visible spectrum in roughly equal proportions.
• Light travelling through a vacuum or a medium is termed white light if it includes all wavelengths of visible light.
• Light travelling through a vacuum or air isn’t visible to our eyes unless it interacts with something.
• The term white light can have two meanings:
• It can refer to a combination of all wavelengths of visible light traveling through space, regardless of observation.
• What a person sees when all colours of the visible spectrum hit a white or neutral-coloured surface.

## Why the sky is blue

Perhaps the most common of atmospheric effects, the blueness of the sky, is caused by the way sunlight is scattered by tiny particles of gas and dust as it travels through the atmosphere.

The sky is blue because more photons corresponding with blue reach an observer than any other colour.

In outer space, the Sun forms a blinding disk of white light set against a completely black sky. The only other light is produced by stars and planets (etc.) that appear as precise white dots against a black background. The sharpness of each of these distant objects results from the fact that photons travel through the vacuum of space in straight lines from their source to an observer’s eyes. In the absence of gas and dust, there is nothing to scatter or diffuse light into different colours and no surfaces for it to mirror or reflect off.

All of this changes when sunlight enters the atmosphere. Here, the majority of photons do not travel in straight lines because the air is formed of gases, vapours and dust and each and every particle represents a tiny obstacle that refracts and reflects light. Each time a photon encounters an obstacle both its speed and direction of travel change resulting in dispersion and scattering. The outcome is that, from horizon to horizon, the sky is full of light travelling in every possible direction and it reaches an observer from every corner.

The following factors help to account for why blue photons reach an observer in the greatest numbers:

• The sky around the Sun is intensely white in colour because vast numbers of photons of all wavelengths make the journey from Sun to an observer in an almost straight line.
• In every other area of the sky, light has to bend towards an observer if they are to see colour. It is this scattering of light that fills the sky with diffuse light throughout the day.
• Longer wavelengths of light (red, yellow, orange and green) are too big to be affected by tiny molecules of dust and water in the atmosphere so scatter the least so few are redirected towards an observer.
• Shorter wavelengths (blue and violet) are just the right size to interact with obstacles in the atmosphere. These collisions scatter light in every possible direction including towards an observer.
• Because blue is relative intense compared with violet in normal conditions and in the absence of the longer wavelengths the sky appears blue.
• However, there is a whole band of wavelengths corresponding with what we simply call blue. As a result, different atmospheric conditions fill the sky with an enormous variety of distinctly different blues during the course of the day.