## Understanding rainbows

To properly understand rainbows involves referring to different fields of enquiry and areas of knowledge.

• The field of optics tells us that rainbows are about the paths that light takes through different media and are the result of reflection, refraction and dispersion of light in water droplets.
• A weather forecaster might explain rainbows in meteorological terms because they depend on sunlight and only appear in the right weather conditions and times of the day.
• A hydrologist, who studies the movement and distribution of water around the planet, might refer to the water cycle and so to things like evaporation, condensation and precipitation.
• A vision scientist will need to refer to visual perception in humans and the biological mechanisms of the eye.
• An optometrist may check for colour blindness or eye disease.

Our DICTIONARY OF LIGHT COLOUR AND VISION assembles terms drawn from these different fields to explore our central interest at lightcolourvision.org which is the interconnections between these three topics.
Whenever terms that appear in the DICTIONARY are used on pages within our LIBRARY OF DIAGRAMS, a blue link appears in the text.

## Velocity

When discussing electromagnetic waves, velocity encompasses both the magnitude and direction of propagation, providing a complete description of the wave’s displacement. On the other hand, speed represents the magnitude of motion but does not consider the direction in which the wave is propagating.

##### Velocity
• Velocity is a vector quantity that refers to the rate at which an object changes its position with respect to time.
• It includes both the magnitude (speed) and direction of an object’s motion.
• Velocity describes the displacement of an object per unit of time in a specific direction.
• Velocity can be positive or negative, representing motion in different directions.
• Velocity is measured in units such as meters per second (m/s), kilometres per hour (km/h), or miles per hour (mph), along with an indication of direction.
##### Speed
• Speed is a scalar quantity that refers to the rate at which an object covers distance.
• It is the magnitude of the displacement of an object per unit of time.
• Speed does not consider the direction of motion, only the rate at which an object moves.
• Speed is always positive or zero, representing the magnitude of motion.
• Speed is measured in units such as meters per second (m/s), kilometres per hour (km/h), or miles per hour (mph).
###### References
• When discussing electromagnetic waves, velocity encompasses both the magnitude and direction of propagation, providing a complete description of the wave’s displacement. On the other hand, speed represents the magnitude of motion but does not consider the direction in which the wave is propagating.
##### Velocity
• Velocity is a vector quantity that refers to the rate at which an object changes its position with respect to time.
• It includes both the magnitude (speed) and direction of an object’s motion.
##### Speed
• Speed is a scalar quantity that refers to the rate at which an object covers distance.
• It is the magnitude of the displacement of an object per unit of time.

## Viewing angle

The viewing angle of a rainbow is the angle between a line extended from an observer’s eyes to a bow’s centre point and a second line extended out towards the coloured arcs.

• In all cases, viewing angle, angular distance and angle of deflection all produce the same value measured in degrees.
###### Viewing angle and rainbows
• Viewing angle refers to the number of degrees through which an observer must move their eyes or turn their head.
• On the vertical plane, the viewing angle is a measure of how far an observer must raise their eyes or head to look from the centre of a rainbow out to the coloured arcs.
• On the horizontal plane, the viewing angle is a measure of how far an observer must look from the centre out to the side to see the coloured arcs.
###### Viewing angle and raindrops
• The idea of a viewing angle for a specific raindrop within a rainbow is nonsense really because they are too small to see. However, the viewing angle for a specific raindrop can be derived from the angle of deflection.
• The angle of deflection measures the degree to which a ray striking a raindrop is bent back on itself in the process of refraction and reflection towards an observer.
• Of all the rays deflected towards an observer by a single raindrop, there is always one that produces the most intense impression of colour for an observer at any specific moment. It is often called the rainbow ray.
• The term rainbow ray refers to the path taken by the deflected ray that produces the most intense colour experience for any particular wavelength of light passing through a raindrop.
• A ray-tracing diagram can calculate which of the rays of a specific wavelength, exiting a raindrop is the rainbow ray.
• If an observer could watch a single raindrop as it falls, they would see its viewing angle decrease and its colour change from red, through intermediate colours, to violet. With each change of viewing angle, colour and wavelength the exact trajectory of the rainbow ray must be recalculated.
###### Find the viewing angle
• To find the viewing angle as you look at a rainbow, trace two lines away from your eyes, one to the centre of the rainbow, and the other to any point on the coloured arcs. The viewing angle is between those two lines, which intersect within the lenses of your eyes.
• If you are not sure where the centre of the rainbow is, imagine extending the ends of the bow until they meet and form a circle. The centre (the anti-solar point) is right in the middle.
• For atmospheric rainbows seen from the ground, the anti-solar point is always below the horizon.
• The coloured arcs of a rainbow form the circumference of circles (discs or cones) and share centres at their anti-solar point.
• The viewing angle is the same whatever point is selected on the circumference of the circular arcs of the rainbow visible above the horizon.
• The viewing angle for a primary bow is between approx. 40.70 and 42.40 from its centre. The exact angle depends on which rainbow colour is selected.
• The viewing angle for a secondary bow is at an angle of between approx. 50.40 and 53.40 when you are looking outwards from its centre.
• The viewing angle can be calculated for any specific colour within a rainbow.
• The centre of a rainbow is always on its axis. The rainbow axis is an imaginary straight line that connects the light source, observer and anti-solar point.
• Considered from an observer’s viewpoint, it is clear that all incident rays seen by an observer run parallel with each other as they approach a raindrop.
• Most of the observable incident rays that strike a raindrop follow paths that place them outside the range of possible viewing angles. The unobserved rays are all deflected towards the centre of a rainbow.
• The viewing angles for all rainbow colours are constants determined by the laws of refraction and reflection.
• The elevation of the Sun, the location of the observer and exactly where rain is falling are all variables that determine where a rainbow will appear.
###### Viewing angle, angular distance and angle of deflection
• The term viewing angle refers to the number of degrees through which an observer must move their eyes or turn their head to see a specific colour within the arcs of a rainbow.
• The term angular distance refers to the same measurement when shown in side elevation on a diagram.
• The angle of deflection measures the degree to which a ray striking a raindrop is bent back on itself in the process of refraction and reflection towards an observer.
• The term rainbow ray refers to the path taken by the deflected ray that produces the most intense colour experience for any particular wavelength of light passing through a raindrop.
• The term angle of deviation measures the degree to which the path of a light ray is bent back by a raindrop in the course of refraction and reflection towards an observer.
• In any particular example of a ray of light passing through a raindrop, the angle of deviation and the angle of deflection are directly related to one another and together add up to 1800.
• The angle of deviation is always equal to 1800 minus the angle of deflection. So clearly the angle of deflection is always equal to 1800 minus the angle of deviation.
• In any particular example, the angle of deflection is always the same as the viewing angle because the incident rays of light that form a rainbow are all approaching on a trajectory running parallel with the rainbow axis.

## Viewing angle

The viewing angle of a rainbow is the angle between a line extended from an observer’s viewpoint to the bow’s anti-solar point and a second line extended towards the coloured arcs of its bow.

• Viewing angle, angular distance and angle of deflection all produce the same value measured in degrees.
• To locate the viewing angle as you look at a rainbow, trace two lines away from your eyes, one to the anti-solar point (the centre of the rainbow) and the other to one of the coloured arcs of the rainbow. The viewing angle is between those two lines, which intersect within the lenses of your eyes.
• To establish where the anti-solar point of a rainbow is, imagine extending the ends of the bow until they meet and form a circle. The anti-solar point is right in the middle and is always below the horizon.
• The coloured arcs of a rainbow form the circumference of circles (discs or cones) and share centres at their anti-solar point.
• The viewing angle is the same whatever point is selected on the section of the circumference of the circular arcs of the rainbow visible above the horizon.
• The viewing angle for a primary bow is between approx. 40.70 and 42.40 from its centre. The exact angle depends upon the rainbow colour selected.
• The viewing angle for a secondary bow is between approx. 50.40 and 53.40 when you are looking at its centre.
• The viewing angle can be calculated for any specific colour within a rainbow.
• The centre of a rainbow is always on its axis. The rainbow axis is an imaginary straight line that connects the light source, observer and anti-solar point.
• Most incident rays striking a raindrop will follow paths that place them outside the viewing angle. The resulting deflected rays pass by an observer and play no part in their observation.
• The viewing angle for all rainbows is a constant determined by the laws of refraction and reflection.
• The elevation of the Sun, the location of the observer and exactly where rain is falling are all variables that determine where a rainbow will appear.
##### Viewing angle, angular distance and angle of deflection
• The viewing angle as described above is a measurement taken from an observer’s point of view and conceives of a rainbow as a three-dimensional object in the real world.
• The viewing angle is the angle to which an observer looks regardless of whether they look towards the top of a rainbow to see a specific colour or sideways to look at the same colour near the horizon.
• Angular distance refers to a measurement on a ray-tracing diagram that represents a rainbow as a two-dimensional object.
• Angular distance measures the same angle as the viewing angle so between the rainbow axis and the position of any specific rainbow colour as it appears on the drawing.
• The angle of deflection also refers to a measurement on a ray-tracing diagram. It takes the same measurement but at a different intersection of lines.
• The angle of deflection measures the degree to which a ray striking a raindrop is bent back on itself in the process of refraction and reflection.

## Viewing angles, angular distance and angles of deflection

###### About viewing angles, angular distance and angles of deflection
• The term viewing angle refers to the angle, measured in degrees, between the direction an observer looks in to see the centre of the rainbow and the direction they look to see a specific colour within the rainbow’s arc.
• The term angular distance refers to the same measurement as the viewing angle, especially when depicted on a side elevation diagram.
• The angle of deflection measures the change in direction that a light ray undergoes as it strikes, refracts into, reflects inside, and refracts out of a raindrop towards an observer.
• The term rainbow ray refers to the path taken by a deflected light ray that results in the most intense colour perception for a specific wavelength of light passing through a raindrop.
• The term angle of deviation measures the change in direction a light ray undergoes due to refraction and reflection inside a raindrop, relative to its original direction towards an observer.
• In any specific case of a light ray passing through a raindrop, the angle of deviation and the angle of deflection are interrelated and their sum equals 1800.
• The angle of deviation is equal to 1800 minus the angle of deflection, and vice versa, so the angle of deflection is equal to 1800 minus the angle of deviation.
• In any specific instance, the angle of deflection is approximately the same as the viewing angle, because the incident light rays that contribute to a rainbow all approach parallel to the axis of the rainbow.

## Virtual photon

A virtual photon is a theoretical concept in particle physics. Virtual photons are thought to be particles that exist for an incredibly brief time and cannot be directly observed. Their existence is inferred through their role in mediating interactions between other particles.

• Virtual photons are thought to play a role in many different physical phenomena, including the electromagnetic force, the weak force, and the strong force.
• A photon is a particle that carries electromagnetic radiation. It is the fundamental unit of light.
• Unlike a real photon, which carries electromagnetic radiation, virtual photons are theorized to be exchanged between charged particles during these interactions. This exchange is believed to be the underlying mechanism behind the electromagnetic force, the weak force, and the strong force.
• Virtual photons are created when two charged particles interact with each other. For example, when two electrons interact with each other, they can exchange a virtual photon. This exchange of a virtual photon causes the electrons to repel each other. The electric force that we observe is thought to be due to the exchange of virtual photons between charged particles.
• Whether a virtual photon is real is a matter of debate among physicists. Some believe that virtual photons are simply a mathematical tool used to calculate the interactions of real photons. Other physicists believe that virtual photons are real particles that exist for a very short period of time.
###### References
• A virtual photon is a theoretical concept in particle physics. Virtual photons are thought to be particles that exist for an incredibly brief time and cannot be directly observed. Their existence is inferred through their role in mediating interactions between other particles.
• Virtual photons are thought to play a role in many different physical phenomena, including the electromagnetic force, the weak force, and the strong force.
• A photon is a particle that carries electromagnetic radiation. It is the fundamental unit of light.

## Visible light

Visible light is the range of wavelengths of electromagnetic radiation perceived as colour by human observers.

• Visible light is a form of electromagnetic radiation.
• Other forms of electromagnetic radiation include radio waves, microwaves, infrared, ultraviolet, X-rays, and gamma rays.
• Visible light is perceived by a human observer as all the spectral colours between red and violet plus all other colours that result from combining wavelengths together in different proportions.
• A spectral colour is produced by a single wavelength of light.
• The complete range of colours that can be perceived by a human observer is called the visible spectrum.
• The range of wavelengths that produce visible light is a very small part of the electromagnetic spectrum.

## Visible light

Visible light refers to the range of wavelengths of electromagnetic radiation that is perceived as colour by human observers. While the range of visible light is generally considered to be 400-700 nm, the exact range of colours perceptible can vary slightly between individuals.

• Visible light is one form of electromagnetic radiation. Other forms of electromagnetic radiation include radio waves, microwaves, infrared, ultraviolet, X-rays, and gamma rays. Visible light ranges from approximately 400 nanometres (nm) for violet to 700 nm for red.
• A human observer perceives visible light as a combination of all the spectral colours between red and violet, as well as a vast range of other colours produced from the blending of different wavelengths in varying proportions.
• A spectral colour is produced by a single wavelength of visible light.
• The complete range of colours that can be perceived by a human observer is called the visible spectrum.
• The range of wavelengths that generate visible light constitutes a small portion of the electromagnetic spectrum.
• Visible light is the range of wavelengths of electromagnetic radiation perceived as colour by human observers.
• Visible light is one form of electromagnetic radiation. Other forms of electromagnetic radiation include radio waves, microwaves, infrared, ultraviolet, X-rays, and gamma rays. Visible light ranges from approximately 400 nanometres (nm) for violet to 700 nm for red.
• A human observer perceives visible light as a combination of all the spectral colours between red and violet, as well as a vast range of other colours produced from the blending of different wavelengths in varying proportions.

## Visible spectrum

The visible part of the electromagnetic spectrum is called the visible spectrum.

• The visible spectrum is the range of wavelengths of the electromagnetic spectrum that correspond with all the different colours we see in the world.
• As light travels through the air it is invisible to our eyes.
• Human beings don’t see wavelengths of light, but they do see the spectral colours that correspond with each wavelength and colours produced when different wavelengths are combined.
• The visible spectrum includes all the spectral colours between red and violet and each is produced by a single wavelength.
• The visible spectrum is often divided into named colours, though any division of this kind is somewhat arbitrary.
• Traditional colours referred to in English include red, orange, yellow, green, blue, and violet.

## Visible spectrum

The visible spectrum is the range of wavelengths of the electromagnetic spectrum that correspond with all the different colours we see in the world.

• Human beings don’t see wavelengths of visible light, but they do see the spectral colours that correspond with each wavelength and colours produced when different wavelengths are combined.
• The visible spectrum includes all the spectral colours between red and violet and each is produced by a single wavelength.
• The visible spectrum is often divided into named colours, though any division is somewhat arbitrary.
• Traditional colours in English include: red, orange, yellow, green, blue, and violet.
• The visible spectrum is continuous, and the human eye can distinguish many thousands of spectral colours.
• The fact that we see distinct bands of colour in a rainbow is an artefact of human colour vision.
• The visible spectrum is a small part of the electromagnetic spectrum.

The visible part of the electromagnetic spectrum is called the visible spectrum.

• The visible spectrum is the range of wavelengths of the electromagnetic spectrum that correspond with all the different colours we see in the world.
• As light travels through the air it is invisible to our eyes.
• Human beings don’t see wavelengths of light, but they do see the spectral colours that correspond with each wavelength and colours produced when different wavelengths are combined.
• The visible spectrum includes all the spectral colours between red and violet and each is produced by a single wavelength.
• The visible spectrum is often divided into named colours, though any division of this kind is somewhat arbitrary.
• Traditional colours referred to in English include red, orange, yellow, green, blue, and violet.

## Vision

Vision, the human visual system, is a complex interplay between various components of the eye, including the cornea, pupil, lens, iris, retina, and optic nerve. It collaborates to capture, focus, and convert light into electrical signals that are transmitted to the brain for visual processing and interpretation.

• Vision begins when light emitted or reflected by an object or scene enters our eyes through the cornea, pupil, and lens.
• The cornea and the lens work together to concentrate and focus light onto the retina, which is the photosensitive layer of cells at the back of the eyeball.
• The iris, located between the cornea and the lens, regulates the amount of light reaching the retina. It also determines eye colour and controls the size of the pupil.
• The retina plays a vital role in converting differences in the wavelength and brightness of incoming light into electrical signals.
• The optic nerve, which exits at the back of the eye, carries these signals to the visual processing areas of the brain.
• Vision, as experienced by human beings, forms the foundation of visual perception.
• Visual perception is the human ability to see and understand our surroundings by virtue of the sensitivity of our eyes to wavelengths of light across the entire visible spectrum, from red to violet.
• Visual perception is linked to eyesight but also encompasses the brain’s capability to interpret and comprehend the information received from our eyes.
• Visual perception is the outcome of visual processing, the complex and dynamic process that involves interactions between various retinal cells, neural pathways, and brain regions, ultimately leading to conscious visual perception.
##### Vision
• When light enters the eye, it interacts with specialized cells called cones in the retina. Cones are responsible for detecting and processing different wavelengths of light, which contribute to our perception of colour.
• The three types of cones, commonly referred to as red, green, and blue cones, respond to different ranges of wavelengths. The combined activity of these cones allows us to perceive a wide range of colours.
• The brain plays a crucial role in the perception of colour. It processes the signals received from the cones and interprets them to create our conscious experience of colour.
• Colour perception is influenced by various factors, including the intensity and quality of light, the surrounding environment, and individual differences in vision.
• Our ability to perceive and differentiate colours provides important cues about the world around us, helping us recognize objects, navigate our environment, and experience the richness of visual stimuli.
###### About trichromatic colour vision (Trichromacy)

Trichromatic colour theory explains how the human eye perceives colour.

• Trichromatic colour theory is based on the existence of three types of light-sensitive cone cells in the retina, each responsive to a different range of colours.
• The colours we perceive result from the combined responses of all three types of cones.
• The sensitivity of cone cells forms the physiological basis for trichromatic colour vision in humans.
• The ability to see colour stems from interactions among the three types of cones, with each cone exhibiting a preference for specific wavelengths within the visible spectrum.
• The three cone types are denoted by the initials L (responsive to long wavelengths), M (responsive to medium wavelengths), and S (responsive to short wavelengths).
• L-type cones exhibit the highest responsiveness to light with long wavelengths, favouring wavelengths around 560 nm.
• M-type cones exhibit the highest responsiveness to light with medium wavelengths, favouring wavelengths around 530 nm.
• S-type cones exhibit the highest responsiveness to light with short wavelengths, favouring wavelengths around 420 nm.
###### References
• Vision, the human visual system, is a complex interplay between various components of the eye, including the cornea, pupil, lens, iris, retina, and optic nerve. It collaborates to capture, focus, and convert light into electrical signals that are transmitted to the brain for visual processing and interpretation.
• Vision begins when light emitted or reflected by an object or scene enters our eyes through the cornea, pupil, and lens.
• The cornea and the lens work together to concentrate and focus light onto the retina, which is the photosensitive layer of cells at the back of the eyeball.
• The iris, located between the cornea and the lens, regulates the amount of light reaching the retina. It also determines eye colour and controls the size of the pupil.
• The retina plays a vital role in converting differences in the wavelength and brightness of incoming light into electrical signals.
• The optic nerve, which exits at the back of the eye, carries these signals to the visual processing areas of the brain.

## Visual perception

Colour is not a property of electromagnetic radiation, but a feature of visual perception by an observer.

## Visual perception

Visual perception is the human ability to see and understand our surroundings by virtue of the sensitivity of our eyes to wavelengths of light across the entire visible spectrum, from red to violet.

• Visual perception is a complex process that relies on the intricate interaction between our eyes, the brain, and the interpretation of light signals. It enables us to perceive various visual attributes such as shapes, sizes, textures, depths, motions, and spatial relationships, all of which contribute to our comprehensive understanding and interpretation of the visual world around us.
• These elements collectively contribute to our comprehensive understanding and interpretation of the visual world around us.
• Visual perception is associated with eyesight but also encompasses the brain’s capacity to interpret information received from our eyes.
• The interpretation of visual information depends on the attributes of visual perception.
##### Visual perception and the electromagnetic spectrum
###### References
• Visual perception is the human ability to see and understand our surroundings by virtue of the sensitivity of our eyes to wavelengths of light across the entire visible spectrum, from red to violet.
• Visual perception is a complex process that relies on the intricate interaction between our eyes, the brain, and the interpretation of light signals. It enables us to perceive various visual attributes such as shapes, sizes, textures, depths, motions, and spatial relationships, all of which contribute to our comprehensive understanding and interpretation of the visual world around us.

## Visual processing

###### Visual processing

Visual processing is a complex and dynamic process that involves interactions between various retinal cells, neural pathways, and brain regions, ultimately leading to conscious visual perception.

Visual processing begins the moment light enters the human eye. It then progresses through multiple stages as signals travel towards the visual cortex, where the neural activity is integrated, resulting in conscious visual experience.

As visual processing begins the retina starts to process information about colors, as well as basic information about the shape and movement associated with those colors. By the end of this stage, multiple forms of information about a visual scene are ready to be conveyed to higher brain regions.

Let’s examine two major forms of processing, trichromatic and opponent-processing, which occur within the eyeball as visual information is gathered from light entering our eyes.

Trichromacy, also known as the trichromatic theory of colour vision, explains how three types of cone receptors in the retina work together with bipolar cells to perform their role in the initial stage of colour processing. Rod cells also play a significant role in this form of processing visual information, particularly in low-light conditions.

Opponent-processing, also known as the opponent-process theory of colour vision, explains the second form of processing. Opponent-processing involves ganglion cells that process the data received from trichromatic processing and combine it with other intercellular activities.

It is interesting to note that as both trichromatic and opponent-process theories developed over the last century, researchers and authors have often pitted one theory against the other. However, both processes are crucial for understanding how colour vision occurs.

Trichromatic theory explains the encoding of visual information when light hits the retina, while opponent-processing explains a subsequent stage of information convergence, assembly, and coding before the data leaves the retina via the optic nerve.

Note that:

• Both trichromatic and opponent-processing occur independently within each retina, without comparing with the other.
• Each eye gathers information from a specific viewpoint, approximately 50 mm to the left or right of the nose.
• The two impressions are later compared and combined to provide us with a single three-dimensional, stereoscopic view of the world, rather than two flattened images.

We can consider the layers of retinal cells involved in trichromatic and opponent-processing as examining, interpreting, and transmitting visually relevant information. However, it would be incorrect to view this as a straightforward linear process due to the intricate neural networking, cross-referencing, and feedback loops within the retina.

## 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.