Intensity

Intensity measures the amount of light energy passing through a unit area perpendicular to the direction of light propagation.

  • Intensity measures the amount of energy carried by a light wave or stream of photons.
  • When light is modelled as a wave, intensity is proportional to the square of the amplitude.
  • When light is modelled as a particle, intensity is proportional to the number of photons present at any given point in time.
  • The intensity of light falls off as the inverse square of the distance from a point light source increases.
  • Light intensity at any given distance from a light source is directly related to the power of the light source and the distance from the source.
  • The power of a light source describes the rate at which energy is emitted and is measured in watts.
  • The intensity of light is measured in watts per square meter (W/m²) and is also commonly expressed in lux (lx).
About intensity and brightness
Intensity
  • Intensity refers to the amount of light energy passing through a unit area perpendicular to the direction of light propagation. It measures the concentration of light energy per unit area. Intensity is typically quantified in units such as watts per square meter (W/m²) or lux (lx). In the case of a point source of light, intensity decreases with distance according to the inverse square law.
Brightness
  • Brightness, on the other hand, refers to the subjective perception of how intense or luminous a light source appears to an observer. It is the quality of being bright or emitting or reflecting a lot of light. Brightness is influenced by factors such as the intensity of the light source, the surface area over which the light is distributed, the spectral composition of the light, and the sensitivity of the human eye. Unlike intensity, which is a physical quantity measured objectively, brightness is a perceptual attribute and can vary from person to person.

Intensity

Intensity measures the amount of light energy passing through a unit area perpendicular to the direction of light propagation.

  • Intensity measures the amount of energy carried by a light wave or stream of photons.
  • When light is modelled as a wave, intensity is proportional to the square of the amplitude.
  • When light is modelled as a particle, intensity is proportional to the number of photons present at any given point in time.
  • The intensity of light falls off as the inverse square of the distance from a point light source increases.
  • Light intensity at any given distance from a light source is directly related to the power of the light source and the distance from the source.
  • The power of a light source describes the rate at which energy is emitted and is measured in watts.
  • The intensity of light is measured in watts per square meter (W/m²) and is also commonly expressed in lux (lx).

Interference

Light interference occurs when two or more light waves interact with one another, resulting in a combination of their amplitudes. The resulting wave may increase or decrease in strength..

  • A simple form of interference takes place when two plane waves of the same frequency meet at an angle and combine.
  • Light interference is often observed as interference patterns, such as seen in supernumerary rainbows.
  • Interference patterns are produced when the energy of waves combines constructively or destructively. For example, waves on a pond can create interference patterns.
    • Constructive interference occurs when the crest of one wave meets the crest of another wave of the same frequency at the same point. The resulting wave is the sum of the amplitudes of the original waves.
    • Destructive interference occurs when the trough of one wave meets the crest of another wave. The resulting wave is the difference between the amplitudes of the original waves.
  • In the field of optics, a classical wave model based on the Huygens–Fresnel principle is commonly used to explain optical interference.
  • In the field of quantum mechanics, another model called the Path Integral formulation, developed by Richard Feynman, is used to explain light interference.
About Interference patterns
  • Two waves meeting on a pond is a classic example of wave interference. When two waves overlap, their crests and troughs can interact in two ways:
    • Constructive interference: If the crests of both waves line up, they reinforce each other, creating a higher crest in the resulting wave. This leads to a more noticeable wave disturbance at that point.
    • Destructive interference: If one wave’s crest overlaps another’s trough, they partially cancel each other out. The resulting wave will have a smaller amplitude (lower crest) or might appear flat at that specific spot.

A two-point source interference pattern is a pattern that results from the superposition of two waves emanating from two different sources that are in phase with each other. The pattern has the following features:

  • Interference fringes: The interference pattern consists of bright and dark fringes, known as interference fringes. The bright fringes represent constructive interference, where the peaks of the two waves coincide, while the dark fringes represent destructive interference, where the peak of one wave coincides with the trough of the other.
  • Equidistant fringes: The interference fringes are equidistant from each other, with the distance between adjacent bright fringes (or adjacent dark fringes) being the same.
  • Central maximum: The central region of the pattern is the brightest, and corresponds to the point where the two waves are in phase and reinforce each other most strongly.
  • Symmetry: The pattern is symmetric about the midpoint between the two sources.
  • Wavelength dependence: The spacing between the fringes depends on the wavelength of the light, with shorter wavelengths producing fringes that are closer together than longer wavelengths.
  • Amplitude dependence: The spacing between the fringes also depends on the amplitude of the waves, with waves of higher amplitude producing fringes that are further apart than waves of lower amplitude.
  • Angle dependence: The angle between the two sources and the observer’s position relative to the sources can affect the interference pattern, causing it to shift or distort.

Interference

Light interference occurs when two or more light waves interact with one another, resulting in a combination of their amplitudes. The resulting wave may increase or decrease in strength.

  • A simple form of interference takes place when two plane waves of the same frequency meet at an angle and combine.
  • Light interference is often observed as interference patterns, such as seen in supernumerary rainbows.
  • Interference patterns are produced when the energy of waves combines constructively or destructively. For example, waves on a pond can create interference patterns.
    • Constructive interference occurs when the crest of one wave meets the crest of another wave of the same frequency at the same point. The resulting wave is the sum of the amplitudes of the original waves.
    • Destructive interference occurs when the trough of one wave meets the crest of another wave. The resulting wave is the difference between the amplitudes of the original waves.

Internal reflection

Internal reflection occurs when light travelling through a medium, such as water or glass, reaches the boundary with another medium, like air, and a portion of the light reflects back into the original medium. This happens regardless of the angle of incidence, as long as the light encounters the boundary between the two media.

  • Internal reflection is a common phenomenon not only for visible light but for all types of electromagnetic radiation. For internal reflection to occur, the refractive index of the second medium must be lower than that of the first medium. This means internal reflection happens when light moves from a denser medium, such as water or glass, to a less dense medium, like air, but not when light moves from air to glass or water.
  • In everyday situations, light is typically both refracted and reflected at the boundary between water or glass and air, often due to irregularities on the surface. If the angle at which light strikes this boundary is less than the critical angle, the light is refracted as it crosses into the second medium.
  • When light strikes the boundary exactly at the critical angle, it neither fully reflects nor refracts but travels along the boundary between the two media. However, if the angle of incidence exceeds the critical angle, the light will undergo total internal reflection, meaning no light passes through, and all of it is reflected back into the original medium.
  • The critical angle is the specific angle of incidence, measured with respect to the normal (a line perpendicular to the boundary), above which total internal reflection occurs.
  • In ray diagrams, the normal is an imaginary line drawn perpendicular to the boundary between two media, and the angle of refraction is measured between the refracted ray and the normal. If the boundary is curved, the normal is drawn perpendicular to the curve at the point of incidence.

Internal reflection

Internal reflection occurs when light travelling through a medium, such as water or glass, reaches the boundary with another medium, like air, and a portion of the light reflects back into the original medium. This happens regardless of the angle of incidence, as long as the light encounters the boundary between the two media.

      • Internal reflection is a common phenomenon not only for visible light but for all types of electromagnetic radiation. For internal reflection to occur, the refractive index of the second medium must be lower than that of the first medium. This means internal reflection happens when light moves from a denser medium, such as water or glass, to a less dense medium, like air, but not when light moves from air to glass or water.
      • In everyday situations, light is typically both refracted and reflected at the boundary between water or glass and air, often due to irregularities on the surface. If the angle at which light strikes this boundary is less than the critical angle, the light is refracted as it crosses into the second medium.
      • When light strikes the boundary exactly at the critical angle, it neither fully reflects nor refracts but travels along the boundary between the two media. However, if the angle of incidence exceeds the critical angle, the light will undergo total internal reflection, meaning no light passes through, and all of it is reflected back into the original medium.
      • The critical angle is the specific angle of incidence, measured with respect to the normal (a line perpendicular to the boundary), above which total internal reflection occurs.
      • In ray diagrams, the normal is an imaginary line drawn perpendicular to the boundary between two media, and the angle of refraction is measured between the refracted ray and the normal. If the boundary is curved, the normal is drawn perpendicular to the curve at the point of incidence.
      • Here are the different outcomes that result from different angles of incidence:
        • At a 00 degree angle of incidence, there is no internal reflection; the light passes straight through the boundary without deviation.
        • As the angle of incidence increases, more and more light is internally reflected and less and less light is refracted at the boundary. This means that less is refracted and so progressively less crosses the boundary into the medium with the lower refractive index.
        • At the critical angle, the light grazes the boundary, and all of it is internally reflected, resulting in no refraction into the second medium.
        • Beyond the critical angle, total internal reflection occurs, and the light is entirely reflected into the first medium.
Example
    • Here is an example. If light travels from water to air where the critical angle is about 48.6 degrees.
      • This means that if light reflects off a fish in a fish tank and then strikes the surface of the water at an angle of less than 48.6 degrees, the angle of incidence determines how much light is internally reflected.
      • If light reflects off a fish in a fish tank and then strikes the water’s surface at an angle of 48.6 degrees or greater, it will experience total internal reflection and no light will pass out of the water and into the air.
    • In reality, light is usually partially refracted and partially reflected because of irregularities in the surface at the boundary. This causes differences in the angle of incidence at different points across the boundary.
  • Here are the different outcomes that result from different angles of incidence:
    • At a 00 degree angle of incidence, there is no internal reflection; the light passes straight through the boundary without deviation.
    • As the angle of incidence increases, more and more light is internally reflected and less and less light is refracted at the boundary. This means that less is refracted and so progressively less crosses the boundary into the medium with the lower refractive index.
    • At the critical angle, the light grazes the boundary, and all of it is internally reflected, resulting in no refraction into the second medium.
    • Beyond the critical angle, total internal reflection occurs, and the light is entirely reflected into the first medium.
Example
  • Here is an example. If light travels from water to air where the critical angle is about 48.6 degrees.
    • This means that if light reflects off a fish in a fish tank and then strikes the surface of the water at an angle of less than 48.6 degrees, the angle of incidence determines how much light is internally reflected.
    • If light reflects off a fish in a fish tank and then strikes the water’s surface at an angle of 48.6 degrees or greater, it will experience total internal reflection and no light will pass out of the water and into the air.
  • In reality, light is usually partially refracted and partially reflected because of irregularities in the surface at the boundary. This causes differences in the angle of incidence at different points across the boundary.

Interneuron

Interneurons are a type of neuron found in the nervous system of animals, including humans, which play a role in processing and communicating information.

  • Interneurons can be classified into different types based on their functions, such as local circuit interneurons and relay interneurons.
  • Local circuit interneurons have short axons and form circuits with nearby neurons to analyse and process information locally.
  • Relay interneurons have long axons and connect circuits of neurons in different regions of the central nervous system, enabling communication and integration of information.
  • Interneurons can be further classified into sub-classes based on their neurotransmitter type, morphology, and connectivity.
  • Interneurons serve as nodes within neural circuits, enabling communication and integration of sensory and motor information between the peripheral nervous system and the central nervous system.

Interneuron

Interneurons are a type of neuron found in the nervous system of animals, including humans, which play a role in processing and communicating information.

  • Interneurons can be classified into different types based on their functions, such as local circuit interneurons and relay interneurons.
    • Local circuit interneurons have short axons and form circuits with nearby neurons to analyse and process information locally.
    • Relay interneurons have long axons and connect circuits of neurons in different regions of the central nervous system, enabling communication and integration of information.
  • Interneurons can be further classified into sub-classes based on their neurotransmitter type, morphology, and connectivity.
  • Interneurons serve as nodes within neural circuits, enabling communication and integration of sensory and motor information between the peripheral nervous system and the central nervous system.
  • The interaction between neurons and interneurons is essential for the proper functioning of the nervous system, enabling the brain to perform complex processes such as perception, cognition, and motor control.
About interneurons and the human eye
  • There are four types of interneurons in the human eye: They are the amacrine cell, bipolar cell, horizontal cell and Müller cell.
  • Interneurons in the human eye form a complex network of interconnections between photoreceptor cells (i.e., rod and cone cells) and retinal ganglion cells.
  • Rod and cone cells are the photoreceptor cells in the human retina that respond to light.
  • Ganglion cells are the retinal neurons that receive and integrate visual information from photoreceptor cells and then transmit it to the brain via the optic nerve.
  • The complex network of interneurons in the human eye plays an important role in the processing and integration of visual information before transmitting it to the brain.
  • This network is also responsible for various visual functions, including spatial filtering, contrast enhancement, and colour opponent processing.

Invisible dimensions of rainbows

A typical atmospheric rainbow includes six bands of colour from red to violet but there are other bands of light present that don’t produce the experience of colour for human observers.

  • It is useful to remember that:
    • Each band of wavelengths within the electromagnetism spectrum (taken as a whole) is composed of photons that produce different kinds of light.
    • Remember that light can be used to mean visible light but can also be used to refer to other areas of the electromagnetism spectrum invisible to the human eye.
    • Each band of wavelengths represents a different form of radiant energy with distinct properties.
    • The idea of bands of wavelengths is adopted for convenience sake and is a widely understood convention. The entire electromagnetic spectrum is, in practice, composed of a smooth and continuous range of wavelengths (frequencies, energies).
  • Radio waves, at the end of the electromagnetic spectrum with the longest wavelengths and the least energy, can penetrate the Earth’s atmosphere and reach the ground but are invisible to human eyes.
  • Microwaves have shorter wavelengths than radio waves, can penetrate the Earth’s atmosphere and reach the ground but are invisible to human eyes.
  • Longer microwaves (waves with similar lengths to radio waves) pass through the Earth’s atmosphere more easily than the shorter wavelengths nearer the visible parts of spectrum.
  • Infra-red is the band closest to visible light but has longer wavelengths. Infra-red radiation can penetrate Earth’s atmosphere but is absorbed by water and carbon dioxide. Infra-red light doesn’t register as a colour to the human eye.
  • The human eye responds more strongly to some bands of visible light between red and violet than others.
  • Ultra-violet light contains shorter wavelengths than visible light, can penetrate Earth’s atmosphere but is absorbed by ozone. Ultra-violet light doesn’t register as a colour to the human eye.
  • Radio, microwaves, infra-red, ultra-violet are all types of non-ionizing radiation, meaning they don’t have enough energy to knock electrons off atoms. Some cause more damage to living cells than others.
  • The Earth’s atmosphere is opaque to both X-rays or gamma-rays from the ionosphere downwards.
  • X-rays and gamma-rays are both forms of ionising radiation. This means that they are able to remove electrons from atoms to create ions. Ionising radiation can damage living cells.
Remember that:
  • All forms of electromagnetic radiation can be thought of in terms of waves and particles.
  • All forms of light from radio waves to gamma-rays can be thought to propagate as streams of photons.
  • The exact spread of colours seen in a rainbow depends on the complex of wavelengths emitted by the light source and which of those reach an observer.

Joule

The joule (J) is the unit of energy, work, and heat in the International System of Units (SI).

  • The joule (J) is the unit of energy, work, and heat in the International System of Units (SI).
  • One joule is equal to the amount of work done when a force of one newton displaces an object by one meter in the direction of that force.
  • It can also be defined as the amount of energy dissipated as heat when an electric current of one ampere flows through a resistance of one ohm for one second.
  • While joules are a fundamental unit, they are a relatively small unit of energy. Therefore, larger units like kilojoules (kJ) or megajoules (MJ) are often used for practical applications.
Electronvolt prefixes
Abbreviated units
Units to Electronvolts
eV to joules (J)
pico-electronvoltpeV1 peV = 1 x 10-12 (eV)
nano-electronvoltneV1 neV = 1 x 10-9 (eV)
micro-electronµeV1 µeV = 0.000001 (eV)
milli-electronvoltmeV1 meV = 0.001 (eV)
electronvolteV1 eV = 1 (eV)
kilo-electronvoltkeV1 keV = 1,000 (eV)
mega-electronvoltMeV1 MeV = 1,000,000 (eV)
giga-electronvoltGeV1 GeV = 1,000,000,000 (eV)1 GeV = 1.60218 x 10-10 (J)
tera-electronvoltTeV1 TeV = 1,000,000,000,000 (eV)1 TeV = 1.60218 x 10-7 (J)
peta-electronvoltPeV1 PeV = 1 x 1015 (eV)1 PeV = 1.60218 x 10-4 (J)
exa-electronvoltEeV1 EeV = 1 x 1018 (eV)1 EeV = 0.160218 (J)

Joule

The joule (J) is the unit of energy, work, and heat in the International System of Units (SI).

  • One joule is equal to the amount of work done when a force of one newton displaces an object by one meter in the direction of that force.
  • It can also be defined as the amount of energy dissipated as heat when an electric current of one ampere flows through a resistance of one ohm for one second.
  • While joules are a fundamental unit, they are a relatively small unit of energy. Therefore, larger units like kilojoules (kJ) or megajoules (MJ) are often used for practical applications.