Spectral power distribution

The spectral power distribution (spectral distribution) of a light or colour stimulus refers to the range, mixture and intensity of wavelengths of light that it produces.

  • A diagram showing the accurate measurement of the spectral power distribution of the light given off (emitted, transmitted, or reflected) by a light source or by a surface provides complete information about that stimulus.
  • The human eye contains three colour receptors (cones), which means that every spectral power distribution is reduced to three sensory quantities that can be described by tristimulus values.
  • Different stimuli can in some cases produce the same colour sensation for an observer. This effect (called metamerism) occurs because each type of cone responds to the distribution of energy across the entire spectral power distribution of a light source.

Spectral power distribution

The spectral power distribution (SPD) provides a detailed profile of the light emitted or reflected by a source across the visible spectrum, typically represented as a graph where the x-axis shows the wavelength (or frequency) and the y-axis shows the intensity or power at each wavelength.

  • Spectral power distribution is usually measured with a spectroscope. These instruments break down the light into its constituent wavelengths, allowing for precise analysis of the light’s spectral composition. This helps with understanding the exact colour of a light source or how it interacts with materials.
  • SPD is critical in defining colour perception. The way the human eye perceives colour is heavily influenced by the distribution of power at various wavelengths, as different combinations of wavelengths will stimulate the cones in our retinas to varying degrees, resulting in a specific colour experience.
  • SPD helps in identifying and comparing light sources. Different light sources, such as sunlight, LED lamps, or incandescent bulbs, have distinct SPDs. For instance, sunlight has a broad, continuous spectrum, while LEDs or fluorescents often have spikes at certain wavelengths, affecting how we perceive colour under these lights.
  • SPD plays a key role in material appearance. When light reflects off a surface, the spectral power distribution of the reflected light reveals how different wavelengths are absorbed or reflected by the material, influencing the material’s colour and brightness.

Spectrum

The visible spectrum refers to the range of colours that the human eye can perceive, typically seen when light is refracted through a prism, water droplets, or similar mediums. It spans wavelengths from approximately 380 nm (violet) to 700 nm (red), with each wavelength corresponding to a specific colour, from violet through blue, green, yellow, and red.

  • The continuous distribution of colours in the visible spectrum consists of a range of wavelengths, rather than distinct, separate colours.
  • A diagram of the visible spectrum is a linear scale displaying the range of colours our eyes can perceive, arranged by their wavelengths with red at one end and violet at the other.
  • This spectrum is naturally produced when light refracts through a prism or raindrops.
  • The continuous distribution of colours in a spectrum arises because visible light consists of a range of wavelengths, rather than distinct, separate colours.
  • Diagrams of spectral colours are usually presented as spectra: elongated linear bands with red at one end and violet at the other, allowing viewers to see as many colour gradations as possible.
  • The process of separating light into its constituent colours is called dispersion.

Spectrum

The visible spectrum refers to the range of colours the human eye can perceive, typically seen when light is refracted through a prism, water droplets, or similar mediums. It spans wavelengths from approximately 380 nm (violet) to 700 nm (red), with each wavelength corresponding to a specific colour, from violet through blue, green, yellow, and red.

  • The visible spectrum consists of a continuous distribution of colours, formed by a range of wavelengths rather than distinct, separate bands. While we commonly refer to colours like red, green, and violet, the transitions between them are gradual, with no sharp boundaries.
  • A diagram of the visible spectrum typically displays this continuous range as a linear scale, arranged by wavelength, with red at the longer wavelength end (around 700 nm) and violet at the shorter wavelength end (around 380 nm). This kind of diagram allows us to see the full gradation of colours the human eye can perceive.
  • The visible spectrum is naturally produced when light is refracted through a prism, raindrops, or similar mediums, splitting the light into its component wavelengths. This process of separating light is known as dispersion. The resulting diagram, often called a spectrum, visually represents the distribution of spectral colours as a smooth, elongated band from red to violet, enabling us to observe the gradual transitions between colours.
  • Although the spectrum contains an infinite number of colours due to its continuous nature, most diagrams illustrate a limited number of distinguishable colours between red, orange, yellow, green, blue, indigo, and violet.

Specular reflection

Objects with smooth surfaces produce specular (mirror-like) reflections because light reflects off their surfaces at consistent angles.

  • All objects obey the law of reflection on a microscopic level.
  • If the irregularities on the surface of an object are smaller than the wavelengths of incident light then reflected light travels away from the surface at consistent angles.
  • When an observer looks at specular reflections (regular reflections), they see mirror-like images on the surface of an object.
About diffuse reflection
  • If the irregularities on the surface of an object are larger than the wavelengths of the incident light, light reflects in all directions and produces diffuse reflections.
  • A diffuse reflection is easily distinguished from the mirror-like qualities of a specular reflection.
  • Diffuse reflection is responsible for the way we perceive the colours and textures of objects.

Specular reflection

Objects with smooth surfaces produce specular (mirror-like) reflections because light reflects off their surfaces at consistent angles.

  • All objects obey the law of reflection on a microscopic level.
  • If the irregularities on the surface of an object are smaller than the wavelengths of incident light then reflected light travels away from the surface at consistent angles.
  • When an observer looks at specular reflections (regular reflections), they see mirror-like images on the surface of an object.
About diffuse reflection
  • If the irregularities on the surface of an object are larger than the wavelengths of the incident light, light reflects in all directions and produces diffuse reflections.
  • A diffuse reflection is easily distinguished from the mirror-like qualities of a specular reflection.
  • Diffuse reflection is responsible for the way we perceive the colours and textures of objects.
  • The combination of specular and diffuse reflections determines the overall appearance of objects in terms of shininess, dullness, or roughness.

Speed & velocity

About speed & velocity

Speed and velocity are not the same. While they are related, there is a key difference between the two:

  • Speed is a scalar quantity that refers to “how fast an object is moving.” It is the rate at which an object covers distance, without considering the direction of motion. It is expressed in units of distance per time, such as meters per second (m/s) or kilometres per hour (km/h).
  • Velocity is a vector quantity that refers to “the rate at which an object changes its position.” It includes both the speed of the object and its direction of motion. It is also expressed in units of distance per time, such as meters per second (m/s) or kilometres per hour (km/h), but with a specified direction.

Speed of light

About the speed of light
  • The speed of light, 299,792,458 meters per second, is the maximum speed at which information can be transmitted through space.
  • The fact that the speed of light is invariant for all observers, regardless of their relative motion, has important implications for our understanding of the behaviour of matter and energy in the universe.
  • The first consequence of E=mc² is that if the speed of light (c) never changes then it is also true that m=E/c² so matter and energy are not distinct and separate entities but are instead different manifestations of the same underlying substance.
  • The fact that the speed of light is invariant forms a key part of Einstein’s theory of relativity, which describes how the behaviour of space, time, and matter are interrelated.
  • The invariance of the speed of light means that the relationship between mass and energy, as described by Einstein’s famous equation E=mc², is a universal relationship that holds true for all observers, regardless of their relative motion.
  • The fact that the speed of light is invariant also forms a key part of Einstein’s theory of relativity, which describes how the behaviour of space, time, and matter are interrelated.
  • The square of the speed of light (c2) appears in the equation because it relates the energy of an object to its mass and shows that a small amount of mass can be converted into a large amount of energy, and vice versa.
  • If the speed of light were different, then the (c2) factor in the equation would be different as well. So the value of (c2) in the equation is a consequence of the nature of energy and mass, and the fact that the speed of light is a fundamental constant in the universe.
  • The square of the speed of light (c2) serves as a conversion factor that relates the mass of an object to its energy content and shows the enormous amount of energy that can be released when a small amount of mass is converted into energy, as in nuclear reactions.
    • The speed of light multiplied by itself = 299,792,458^2 = 89,875,517,873,681,764

Speed of light

The speed (or velocity) of a light wave is a measurement of how far it travels in a certain time.

  • The speed of light is measured in metres per second (m/s).
  • Light travels through a vacuum at 300,000 kilometres per second.
  • The exact speed at which light travels through a vacuum is 299,792,458 metres per second.
  • Light travels through other media at lower speeds.
  • A vacuum is a region of space that contains no matter.
  • Matter is anything that has mass and occupies space by having volume.
  • When discussing electromagnetic radiation the term medium (plural media) is used to refer to anything through which light propagates including empty space and any material that occupies space such as a solid, liquid or gas.
  • In other contexts empty space is not considered to be a medium because it does not contain matter.

Speed of light

The speed of light is a measurement of how far a light wave travels in a certain amount time.

  • The speed of light is typically measured in metres per second (m/s).
  • In a vacuum, light travels at approximately 300,000 kilometres per second, or more precisely, 299,792,458 metres per second.
  • Light moves at slower speeds when passing through different media.
  • A vacuum is a region of space that contains no matter.
  • Matter refers to anything that has mass and occupies space (i.e., it has volume).
  • When discussing electromagnetic radiation, the term medium (plural: media) refers to anything through which light propagates, including empty space and any material such as a solid, liquid, or gas.
  • In other contexts, empty space is not considered a medium because it lacks matter.
  • Light itself can be described as a wave that carries energy.
  • When light interacts with matter, it can behave like particles called photons.
  • These photons are massless particles that travel at the speed of light. They carry energy and momentum in packets, not as continuous values.
  • In science, this concept is called quantization, which means certain properties can only exist in specific amounts.
  • For photons, this means their energy and momentum come in distinct, separate packets rather than a continuous range.
About speed & velocity

Speed and velocity are not the same. While they are related, there is a key difference between the two:

  • Speed is a scalar quantity that refers to “how fast an object is moving.” It is the rate at which an object covers distance, without considering the direction of motion. It is expressed in units of distance per time, such as meters per second (m/s) or kilometres per hour (km/h).
  • Velocity is a vector quantity that refers to “the rate at which an object changes its position.” It includes both the speed of the object and its direction of motion. It is also expressed in units of distance per time, such as meters per second (m/s) or kilometres per hour (km/h), but with a specified direction.

Speed of light & black holes

About the speed of light and black holes
  • The speed of light squared (c^2) is related to the energy required to create a black hole through Einstein’s famous equation E=mc^2, where E is the energy of a system, m is its mass, and c is the speed of light in a vacuum.
  • This equation shows that there is an equivalence between mass and energy and that a certain amount of energy can be converted into a certain amount of mass, and vice versa.
  • When matter is compressed to a small enough volume, it can create a black hole. The minimum amount of mass required to form a black hole is called the Schwarzschild radius, which is proportional to the mass of the object. The equation for the Schwarzschild radius is:
    • R = 2GM/c^2
    • where R is the Schwarzschild radius, G is the gravitational constant, M is the mass of the object, and c is the speed of light in a vacuum.
  • From this equation, we can see that the speed of light squared is related to the energy required to create a black hole because the more energy that is compressed into a smaller volume, the greater the mass of the object will be, and the larger the Schwarzschild radius will be. Therefore, the greater the amount of energy required to create a black hole, the larger the value of c^2 will be in the equation for the Schwarzschild radius.

Speed of light & Planck scale

About the speed of light and Planck scale
  • The Planck scale is the scale at which the effects of gravity are expected to become comparable to the other fundamental forces of nature, and it is defined by the Planck length, Planck time, and Planck energy. These values are incredibly small and represent the smallest possible length, time, and energy that can exist in the universe according to our current understanding of physics.
  • Interestingly, the speed of light squared is related to the Planck energy through the famous equation E=mc^2. This equation shows that energy (E) is equal to mass (m) times the speed of light squared (c^2). At the Planck energy scale, which is around 1.22 × 10^19 GeV (gigaelectronvolts), the energy required to create a black hole is reached.
  • Moreover, the Planck length can be derived from fundamental constants including the speed of light (c), the gravitational constant (G), and the reduced Planck constant (ħ), and is approximately equal to 1.616 x 10^-35 meters. Therefore, the speed of light squared also plays a role in the definition of the Planck length as it is one of the fundamental constants used to derive it.
  • In summary, the speed of light squared is related to the Planck scale through its connection to energy, as well as its role in the definition of the Planck length.

Speed of light waves & photons

About the speed of light waves & photons
Speed of light waves
  • The speed of a light wave is a measurement of how far it travels in a certain time.
  • The speed of light is usually measured in metres per second (m/s).
  • Light travels through a vacuum at a bit less than 300,000 kilometres per second.
  • The exact speed at which light travels through a vacuum is 299,792,458 metres per second.
  • Light travels through other media at lower speeds.
  • A vacuum is a region of space that contains no matter.
  • Matter is anything that has mass and occupies space by having volume.
  • When discussing electromagnetic radiation the term medium (plural media) is used to refer to anything through which light propagates including empty space and any material that occupies space such as a solid, liquid or gas.
  • In other contexts, empty space is not considered to be a medium because it does not contain matter.
  • When light is described in terms of photons rather than waves the following points are important:
Speed of photons
  • Light exhibits wave-particle duality, meaning it can be described as both a wave and a particle (photon).
  • Photons are massless particles that travel at the speed of light.
  • Photons carry energy and momentum in quantized discrete units.
  • “Quantized discrete units” refers to the way energy and momentum are carried by photons.
  • In quantum mechanics, certain physical properties, such as energy and momentum, are quantized, meaning they can only take specific discrete values rather than a continuous range of values.
  • For photons, this means that their energy and momentum come in distinct, non-continuous packets or “units.”

Standard Model

The Standard Model is the theoretical framework that describes the fundamental particles of nature and the forces that act between them.

  • The Standard Model is a quantum field theory, which means that it uses the principles of quantum mechanics to describe the behaviour of matter and energy at the atomic and subatomic levels.
  • The Standard Model is based on two fundamental theories:
    • Quantum mechanics provides a description of the physical properties of nature as interactions between fields of energy at the scale of atoms and subatomic particles. It is the foundation of all quantum physics.
    • Special relativity is a theory of space and time developed by Albert Einstein in 1905. It states that:
      • The laws of physics are invariant (i.e., identical) in all inertial frames of reference.
      • The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source or observer.
  • The Standard Model describes three of the four fundamental forces:
  • Despite its success, the Standard Model has a major limitation: it doesn’t describe gravity. This is because gravity is not compatible with the principles of quantum mechanics at very small scales. Scientists are still searching for a more comprehensive theory, sometimes called a “Theory of Everything,” that can unify the Standard Model with gravity.
  • The Standard Model describes 17 fundamental particles
    • Quarks: Up, down, charm, strange, top, and bottom.
    • Leptons: Electron, muon, tau, and their 3 corresponding neutrinos.
    • Bosons: Photon, gluon, W and Z bosons, and the Higgs boson.
  • Arguably, the Standard Model stands as the most successful theory created so far by human beings in our attempts to comprehend the totality of existence – the Universe, the world around us, and every aspect of our own physical being.
  • Whilst the model has been able to explain the presence of three of the the four fundamental forces, the behaviour of subatomic particles, and the structure of the atom, it remains a work in progress, with physicists continuously seeking to refine it.
  • The following scientists have received a Nobel Prize for their work on the Standard Model:
    • Richard Feynman, Julian Schwinger, and Yoichiro Nambu (1965 Nobel Prize in Physics) for their work on quantum electrodynamics.
    • Murray Gell-Mann (1969 Nobel Prize in Physics) for his classification of elementary particles.
    • Steven Weinberg, Sheldon Glashow, and Abdus Salam (1979 Nobel Prize in Physics) for their unification of the weak and electromagnetic forces.
    • Peter Higgs and François Englert (2013 Nobel Prize in Physics) for their discovery of the Higgs boson.

Standard Model

The Standard Model is a quantum field theory, which means it uses the principles of quantum mechanics to describe the behaviour of matter and energy at the atomic and subatomic levels.

  • The Standard Model is based on two fundamental theories:
    • Quantum mechanics describes the physical properties of nature as interactions between fields of energy at the scale of atoms and subatomic particles. It is the foundation of all quantum physics.
  • Special relativity is a theory of space and time developed by Albert Einstein in 1905. It states that:
    • The laws of physics are invariant (i.e., identical) in all inertial frames of reference.
    • The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source or observer.

Stellar light

Stellar light is the term used to describe the electromagnetic radiation emitted by stars, primarily due to the nuclear fusion of hydrogen atoms occurring within their cores.

  • Unlike traditional sources of light on Earth, stars ignite with a far more powerful process – nuclear fusion.
  • Deep within their incredibly dense and hot cores, immense pressure and temperatures fuel nuclear fusion.
  • This process forces hydrogen atoms to merge into heavier elements, primarily helium, releasing tremendous energy.
  • A fraction of this energy escapes the star as the radiant light we call sunlight and starlight.

Strong Nuclear force

The strong nuclear force is one of the four fundamental forces in nature. The other forces are the electromagnetic force, the weak nuclear force and gravity.

  • The strong nuclear force is the strongest of the four fundamental forces of nature but only acts over very small distances, about the size of an atom’s nucleus. This short-range force is about 100 times stronger than the electromagnetic force, 106 times stronger than the weak nuclear force, and 1038 times stronger than gravity.
  • The strong nuclear force is the fundamental force that binds matter together and is responsible for holding together protons and neutrons which are the subatomic particles within the atomic nucleus.
  • The strong nuclear force counteracts the electrical repulsion between protons, which would otherwise push the positively charged protons apart.
  • The strong nuclear force plays a crucial role in nuclear reactions, allowing the release of tremendous energy in processes like nuclear power generation and nuclear weapons.

Strong nuclear force

The strong nuclear force is one of the four fundamental forces in nature. The other forces are the electromagnetic force, the weak nuclear force and gravity.

  • The strong nuclear force is the strongest of the four fundamental forces of nature but only acts over very small distances, about the size of an atom’s nucleus. This short-range force is about 100 times stronger than the electromagnetic force, 106 times stronger than the weak nuclear force, and 1038 times stronger than gravity.
  • The strong nuclear force is the fundamental force that binds matter together and is responsible for holding together protons and neutrons which are the subatomic particles within the atomic nucleus.
  • The strong nuclear force counteracts the electrical repulsion between protons, which would otherwise push the positively charged protons apart.
  • The strong nuclear force plays a crucial role in nuclear reactions, allowing the release of tremendous energy in processes like nuclear power generation and nuclear weapons.

Subjective experience of colour

About the subjective experience of colour
  • The perception of colour is a highly subjective experience.
  • Several factors determine the specific colour an observer sees, including:
    • The environment in which colours are observed, the type of object, and colour associations.
    • The colour of nearby objects.
    • Well-being, including health, medications, mood, emotions, or fatigue, can all affect the eyes, vision, and perceptions of an observer.
  • Different observers may see colour differently because of life experience including educational, social and cultural factors.
  • The term observer has distinct and different meanings within the fields of special relativity, general relativity, quantum mechanics, thermodynamics and information theory.

Substance

A substance is a type of matter with uniform properties throughout. This means that a substance sample will have the same characteristics regardless of its size.

  • One kind of substance is a chemical substance. A chemical substance is a specific type of matter with molecules with the same structure and composition.
  • Chemical bonds hold these molecules together. Substances cannot be separated into their parts (elements or compounds) without breaking these chemical bonds.
  • Substances can be generally classified into two main categories:
    • Elements: The simplest form of a substance, elements are made up of only one type of atom.
    • Compounds: These substances are formed when two or more elements chemically bond together.