Dictionary category: Definitions

• Optics studies the behaviour of electromagnetic radiation in the visible, ultraviolet, and infrared regions of the electromagnetic spectrum.
• Some fields of optics also study the behaviour and properties of other forms of electromagnetic radiation such as X-rays and microwaves.
• The observation and study of optical phenomena offer many clues as to the nature of light.
• Optical phenomena include absorption, dispersion, diffraction, polarization, reflection, refraction, scattering and transmission.
• Optics explains the appearance of rainbows, how light reflects off mirrors, how light refracts through glass or water, and why light separates into a spectrum of colours as it passes through a prism.

Contemporary optics

• Most optical phenomena can be accounted for using the classical electromagnetic description of light (wavelength, frequency and intensity) but they can also be modelled as particles called photons.
• Optics is both a field of physics and an area of engineering. It has been used to create many useful devices, including eyeglasses, cameras, telescopes, and microscopes. Many of these devices are based on lenses, which can focus light and produce images of objects that are larger or smaller than the original.
• New discoveries are being made in the field of optics For example, The first working fibre-optic data transmission system was demonstrated in 1965. Less than 60 years later, fibre optics are now used to send vast amounts of data through thin optical fibre around the world.
• Contemporary specializations within the field of optics include:
  • Geometrical optics is a branch of optics that deals with the behaviour of light as a collection of rays that propagate in straight lines and are subject to reflection and refraction.
  • Physical optics is a branch of optics that describes the behaviour of light as both a wave and a particle and includes wave phenomena such as diffraction and interference that are not explained by geometrical optics.
  • Quantum mechanics is a branch of physics that describes the behaviour of light as both a wave and a particle and investigates the interactions between light and matter.

• Oscillation is a characteristic of waves, including electromagnetic waves.
• Examples of oscillation include the side-to-side swing of a pendulum and the up-and-down motion of a spring with a weight attached.
• Electromagnetic waves oscillate due to the transmission of energy by their electric and magnetic fields.
• An oscillating movement is typically around a point of equilibrium and the motion repeats itself around an equilibrium position.

• Particle physics is an experimental sub-field of quantum mechanics often associated with the Large Hadron Collider at CERN.
• The Large Hadron Collider is a particle accelerator, which collides particles at high energies. These collisions create new particles, which are then studied by detectors. The detectors measure the properties of the new particles, such as their mass, energy, and charge.
• The Standard Model serves as the theoretical framework employed by particle physicists to investigate fundamental forces and particles.
• Among the most important discoveries of particle physics was the discovery of the photon and the dual nature of light (both a wave and particle).

• Our ability to perceive and distinguish between colours is crucial to how we experience and understand the world.
• Perceived colour is influenced by the range and mixture of wavelengths and intensities of light that enter the eye.
• Perceived colour can be influenced by the properties of light, objects, and the attributes of visual perception.
• Colour perception tends to prioritize information that is important to an observer, but it may not always be objectively accurate.
• The perceived colour of an object can be influenced by factors, such as the size, shape, and structure of objects, their position and orientation, and the direction of incident light.
• Colour perception can be described by chromatic colour names (such as pink, orange, brown, green, blue, and purple) and achromatic colour names (such as black, grey or white).
• Perceived colour is often a combination of chromatic and achromatic content.
• The state of adaptation of an observer’s visual system can affect colour perception, such as when fatigued cells in the retina produce after-images.
• An observer’s expectations, priorities, current activities, recollections, and previous experiences can all influence perceived colour.
• The International Commission on Illumination (CIE) defines perceived colour as having three main characteristics: hue, brightness (or lightness), and colourfulness (or saturation/chroma).
• Here at lightcolourvision.org we often characterise colour in terms of hue, saturation and brightness and so align our discussions with the HSB colour model.

Here is a short explanation of phosphorescence:

• Excitation: When a phosphorescent material is exposed to light, electrons within the material absorb the photons’ energy and move to a higher energy state (become excited).
• Trapped State: Unlike fluorescence, where electrons immediately return to their ground state and emit light, in phosphorescence, the excited electrons get “trapped” in a forbidden triplet state. This means they can’t directly transition back to their lower energy state.
• Gradual Release: Over time, the trapped electrons slowly find their way back to the ground state, releasing the stored energy as light. This process is much slower than fluorescence, which is why phosphorescence produces that lingering afterglow.

Key Points:

• Duration: Phosphorescence can last for seconds, minutes, or even hours, unlike fluorescence which ends almost immediately after the light source is removed.
• Excitation Source: Phosphorescent materials typically need light with shorter wavelengths for excitation, such as ultraviolet light.

Examples:

• Glow-in-the-dark toys: These are coated with phosphorescent materials.
• Safety signs: Phosphorescent signs stay visible in low light conditions.
• Watch dials: Some watch dials used to use phosphorescent paint for nighttime visibility (this has been replaced by safer alternatives in modern watches).

Photoluminescence in three Steps

1. Absorption: Light excites electrons in a material, pushing them to higher energy levels.
2. Relaxation: Excited electrons gradually lose energy.
3. Light Emission: Lost energy is emitted as light of a different wavelength (usually longer).

Key Points

• Emitted light often has lower energy (longer wavelength) than absorbed light due to energy loss.
• Different types of photoluminescence exist based on relaxation mechanisms:
  • Fluorescence: Quick relaxation, emitting light soon after absorption.
  • Phosphorescence: Slower relaxation, emitting light later, creating a “glow” effect.
  • Chemiluminescence: Light emission due to a chemical reaction. The reaction can be initiated by various factors, including but not limited to light absorption.

Applications

• Fluorescent lamps convert ultraviolet light to visible light.
• LEDs use electroluminescence (photoluminescence triggered by electricity).
• Biological markers help visualize structures or processes in cells.
• Quantum dots have bright, tunable photoluminescence for displays and solar cells.

• Measuring human visual responses to light is not straightforward because the eye is a complex and intricate organ.
• An internationally recognized system of measurements, known as the CIE system, was established in 1931 by the Commission Internationale de l’Eclairage (CIE).
• The Commission established the typical spectral responsiveness of the human eye to wavelengths across the visible spectrum and compiled the data into a photopic curve.
• The CIE’s photopic curve shows that, in bright light, the strongest response of the human eye is to the colour green with less sensitivity towards the spectral extremes, red and violet.
• A second set of measurements of the typical responsiveness of the human eye to wavelengths across the visible spectrum at low levels of light, (where determining colour differences is difficult), resulted in data compiled into the scotopic curve.
• Having defined the spectral response of the human eye, the CIE sought a standard light source to measure luminous intensity.
• Luminous intensity is a measure of how bright a light source appears to the human eye, and it is typically used to describe the brightness of light sources such as light bulbs, lamps, and LEDs.
• The first source, which led to the development of the terms footcandle and candlepower, was a specific type of candle commonly used in the 18th and 19th centuries before standardised artificial light sources were developed.
• In 1948, the standard was redefined for better repeatability. It was named the International Candle and defined as the amount of light emitted from a given quantity of melting platinum.

• Thinking of photons as particles is useful for understanding the quantum nature of light.
• In the world of quantum physics, photons are the fundamental constituents of all forms of electromagnetic radiation, including light. They serve as the carriers of the electromagnetic force.
• Photons are elementary particles that have no mass and no electric charge. They are the quanta of the electromagnetic field, which is the fundamental field that describes electromagnetic interactions. Electromagnetic radiation, including light, is a manifestation of the electromagnetic field.
• Photons are the carriers of electromagnetic force because they are the only particles that can mediate electromagnetic interactions. When two charged particles interact electromagnetically, they exchange photons. The exchange of photons gives rise to the electromagnetic force.<
• Photons have no rest mass and always travel at the speed of light in a vacuum.
• Photons exhibit both wave-like and particle-like properties, a characteristic referred to as wave-particle duality. This duality is inherent to quantum particles, causing light to behave as a wave under certain conditions, as both waves and photons in others, and strictly as particles in yet others.

Photons properties

• Photons, the elemental particles of electromagnetic radiation, possess distinct properties:
  • Energy: The energy of a photon is contingent upon its frequency or wavelength. Higher frequencies correspond to greater energy levels.
  • Number: Intensity or brightness dictates the number of photons present in electromagnetic radiation. Higher intensities correlate with larger photon counts.
  • Direction and Polarization: Photons travel in straight paths, but interactions with matter can alter their direction. Additionally, photons can exhibit polarization, indicating the orientation of their electric and magnetic fields.
  • Speed: Photons travel at the speed of light, an astounding 299,792,458 meters per second in a vacuum.

Photons and mass

•  The statement above about zero rest mass can be broken down as follows:
  • According to the theory of relativity, any object that has mass needs energy to accelerate.
  • The amount of energy required to accelerate an object increases as the object’s mass increases.
  • Photons are unique in that they have zero rest mass and this means they do not require any energy to be accelerated.
  • As a result, they always move at the speed of light in a vacuum.
  • So photons always travel at approximately 299,792 kilometres per second and, when undisturbed, they never decelerate or come to a halt.

Energy of photons, wavelength, frequency and colour

• The energy of a photon (its photon energy) is intrinsically linked to its wavelength and frequency, and in perceptual terms, to its colour.
  • Photon Energy: The energy of a photon, E, is given by the equation E=hf, where h is Planck’s constant and f is the frequency of the photon. So, a photon with a higher frequency has higher energy.
  • Frequency and Wavelength: Frequency (f) and wavelength (λ) are related by the speed of light (c), through the equation c=fλ. So, photons with a higher frequency have a shorter wavelength, and photons with a lower frequency have a longer wavelength.
  • Colour Perception: In terms of colour perception, different frequencies and wavelengths of electromagnetic energy are perceived as different colours.
  • For example, photons with high energy (high frequency, short wavelength) are perceived as blue/violet, while photons with lower energy (low frequency, long wavelength) are perceived as red. The range of frequencies (or wavelengths) that human eyes can detect is known as the visible light spectrum.

Photons and interaction with charged particles

• Photons can interact with charged particles such as electrons within atoms. In such events, they can either be absorbed, resulting in the elevation of the particle to a higher energy state or be emitted when a particle transitions from a higher energy state to a lower one.
• A higher energy state refers to a quantum state or level of an atomic or subatomic system in which an electron or particle has absorbed energy and moved to a more excited or elevated position, typically farther from the nucleus or centre of the system.

Photons and interaction with matter

• Photons can engage with matter through various processes. They can be scattered, absorbed, or emitted during interactions with atoms and molecules. These processes are crucial for a range of phenomena from the heating of surfaces under sunlight to the transmission of information in fibre optic cables.

Photons and polarization

• Photons can be polarized. This means their electric and magnetic fields can oscillate in a specific orientation. Polarization is used in various applications, from LCD screens to polarized sunglasses, and is also a significant aspect of certain quantum mechanical phenomena.

Photons and their Energy, Frequency, Wavelength and Momentum

• The energy of a photon determines its frequency, wavelength and momentum. This energy can be transferred during interactions, leading to phenomena like fluorescence and the photoelectric effect. In the visible spectrum, different energies (and therefore frequencies and wavelengths) correspond to different colours of light.
• The energy of a photon is directly proportional to its frequency. This means that photons with higher frequencies have more energy. The energy of a photon is also inversely proportional to its wavelength. This means that photons with longer wavelengths have less energy. The momentum of a photon is inversely proportional to its wavelength. This means that photons with shorter wavelengths have more momentum.

Photons and wave-particle duality

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

• The higher the photon’s frequency, the higher its energy. Equivalently, the shorter the photon’s wavelength, the higher its energy.
• Photon energy is determined solely by the photon’s frequency and wavelength.
• Other factors, such as the intensity of the radiation, do not affect the energy of individual photons. In other words, two photons of light with the same frequency have the same energy, regardless of their source. even if one was emitted from a wax candle and the other from the Sun.
• The electronvolt (eV) and the joule are the units commonly used to express the energy of photons.
• The energy of a photon can also be expressed:
  • In terms of its wavelength or frequency using Planck’s constant (h). E = hν = hc/λ, where E is the energy, ν is the frequency, λ is the wavelength, and c is the speed of light.
  • As a quantum of electromagnetic radiation.

• One of the most common interactions used to explain the link between electromagnetism and light (including visible light and other parts of the spectrum) is the photon-electron interaction.
• The specific outcome of a photon-electron interaction depends on the photon’s energy and the electron’s state. For example, if the photon has enough energy, it can free a bound electron from the atom. This is known as the photoelectric effect.
• If the photon does not have enough energy to eject the electron, it can be scattered by the electron. Compton scattering involves high-energy photons, like X-rays or gamma rays, where the photon transfers part of its energy to the electron. The photon loses energy (shifts to a longer wavelength) and changes direction, while the electron gains kinetic energy.
• On absorption of a photon by an electron, the electron gains energy and transitions to a higher energy level – a higher orbital around the nucleus of the atom.
• When an electron scatters a photon elastically, such as in Rayleigh scattering, the photon alters its trajectory but retains its energy, and the electron’s energy level remains unaffected. In Compton scattering, however, the electron gains energy.
• A photon can transfer all of its energy to an electron if it has more energy than the electron’s binding energy. In this case, the electron will be ejected from the atom with excess kinetic energy.
• The amount of energy a photon can transfer to an electron is capped by the photon’s own energy. A photon cannot impart more energy to an electron than it possesses.
• The likelihood of a photon being absorbed by an electron depends on both the photon’s energy and the electron’s energy level. Absorption occurs when the photon’s energy exactly matches the difference between two energy levels (resonant absorption). Generally, higher photon energy increases the absorption likelihood, while higher electron energy levels tend to decrease the absorption probability due to fewer available transitions.
• The likelihood of photon scattering is influenced by the photon’s energy and the electron’s energy state. In Compton scattering, the angle of photon-electron collision affects the energy loss of the photon. Polarization of the photon and electron spin can also influence specific types of scattering, but spin is less central in general scattering processes.

• Examples of a photons-electron interaction include:
  • Photoelectric Effect: When a photon with adequate energy impacts an electron, the electron can be expelled from the atom. Called the photoelectric effect, the photon’s energy must exceed the electron’s binding energy within the atom.
  • Compton Scattering: In a collision between a photon and an electron, the photon can scatter. The photon might relinquish energy during the collision, and the electron can acquire a portion of the photon’s energy.
  • Chromophore excitation: The photon-chromophore interaction accounts for the observable colour of objects.
    • The interaction between photons and chromophores is more intricate than photon-electron interaction. It encompasses energy redistribution among all electrons in a molecule and can result in various outcomes such as fluorescence, phosphorescence, and energy transfer.
    • The interaction between photons and chromophores is generally referred to as molecular excitation or chromophore excitation, distinct from photon-electron interaction but can still be considered a type of photon-electron interaction since it involves the interaction of photons with the electrons in chromophore molecules.

• The standard photopic curve used in the CIE 1931 colour space is based on the photopic luminosity function, which describes the average sensitivity of the human eye to different wavelengths of light under normal, bright lighting conditions.
• A photopic luminosity function is a mathematical function used to derive the photopic curve from the CIE 1931 colour space.
• The CIE 1931 colour space is a standardized system for describing colours based on human colour perception. It was developed by the International Commission on Illumination (CIE) in 1931 and is still widely used today.
• In low light conditions, the sensitivity of the human eye to light changes, and the scotopic curve is used to describe the response of the eye to light.
• Scotopic and photopic curves have different units of measurement.
  • A photopic curve uses units of luminous flux, which is a measure of the total amount of visible light emitted by a source.
  • A scotopic curve, on the other hand, uses units of luminous intensity, which is a measure of the brightness of a light source per unit of solid angle.

The retinal pigment epithelium (RPE) is a layer of pigmented cells located between the retina and the choroid of the human eye that supports the photoreceptor cells (rods and cones).
<ul>
<li>The RPE plays a critical role in providing nutrients, removing waste products, and regenerating visual pigments needed for photoreceptor function.</li>
<li>The RPE is firmly attached to the underlying Bruch’s membrane of the choroid on one side, but less firmly connected to the photoreceptor cells of the retina on the other. This weaker attachment can contribute to retinal detachment.</li>
<li>The choroid is a vascular layer rich in blood vessels and connective tissue that lies between the retina and the sclera. It provides oxygen and nutrients to the outer layers of the retina and parts of the sclera, supporting the function of the retinal pigment epithelium and photoreceptors.</li>
</ul>

• A pixel, also known as a picture element, is a physical point in a digital image and the smallest addressable element of a display device.
• In the editing process, a pixel is the smallest controllable element of a digital image.
• Many digital displays, including LCD screens, contain LEDs arranged in a grid pattern and emit light when an electrical current is passed through them, allowing them to display different colours and brightness levels.
• OLED displays use a different technology that uses organic compounds that emit light when an electrical current is passed through them.
• The RGB colour model is commonly used for still images displayed on digital screens, such as computer monitors and televisions.
• In the RGB colour model, each pixel is composed of three subpixels that control the red, green, and blue colour channels.
• By varying the light emitted by an LED, every pixel can display a wide range of colours and shades, allowing for the creation of highly detailed and vibrant images on screen.
• The resolution of a digital screen, or the number of pixels it can display, is an important factor in determining its overall image quality and sharpness.
• Higher-resolution screens can display more pixels per inch (PPI), resulting in smoother, more detailed images with less visible pixelation.
• Newer display technologies may use variations of the RGB colour model to display still images, such as RGBW (Red, Green, Blue, White) or RGBY (Red, Green, Blue, Yellow).

• The Planck constant is a measure of the smallest possible amount of energy that can be carried by a single quantum of electromagnetic radiation (a photon).
• The Planck constant is also related to the wavelength of a photon by the equation E = hf, where E is the energy of the photon, f is its frequency, and h is the Planck constant.
• The equation, energy (E) = Planck constant (h) x frequency (f), allows the quantity of energy associated with electromagnetic radiation to be calculated if the frequency is known.
• The Planck constant is used extensively in modern physics, particularly in the fields of quantum mechanics, atomic physics, and condensed matter physics.
• It plays a crucial role in determining the energy levels of atoms and molecules, as well as the behaviour of subatomic particles such as electrons and photons.
• The value of the Planck constant is approximately 6.626 x 10^-34 joule-seconds (Js).

• Polarization can be induced in light waves by various means, such as reflection, refraction, and scattering.
• There are several types of polarization, including circular, elliptical and plane polarization.
  • Circular polarization refers to waves that rotate in circles as they propagate, with the electric and magnetic fields perpendicular to each other.
  • Elliptical polarization combines linear and circular polarization, in which the wave oscillates in an elliptical pattern.
  • Plane polarization (sometimes called linear polarization) refers to waves that oscillate in a single plane, such as waves that are vertically or horizontally polarized.

Plane polarization in detail

• Plane polarizing filters only allow waves with a certain orientation of their electric field to pass through.
• Plane polarizing filters block all the waves where the electric field is not orientated with the polarizing plane.

To visualize plane polarization:

• Imagine pushing a large sheet of card through a window fitted with close-fitting vertical bars.
• Only by aligning the card with the slots between the bars can it pass through. Align the card at any other angle and its path is blocked.
• Now substitute the alignment of the electric field of an electromagnetic wave for the sheet of card, and plane polarization for the bars on the window.

Causes of polarization

• • Objects and phenomena that can cause plane polarization include:
    • Polarizers (polarizing filters): Polarizers selectively transmit light of a certain polarization while blocking light of other polarizations. They can be made from materials such as polarizing film or a grid of fine wires.
    • Reflection: When light reflects off a non-metallic surface at an angle, it can become plane-polarized. This is because the electric field of the reflected light is perpendicular to the plane of incidence.
    • Scattering: When light is scattered by small particles, such as dust or molecules in the atmosphere, it can become polarized. This is because the scattered light waves are preferentially oriented in certain directions.
    • Liquid crystals: Liquid crystals are materials that can change their optical properties in response to an applied electric field. They are used in displays such as LCD screens to selectively polarize light in order to create an image.

• In the context of light, polychromatic refers to light that contains multiple wavelengths, each corresponding to a different colour in the visible spectrum. For example, white light is polychromatic because it is a combination of all the colours (wavelengths) within the visible spectrum.
• Sunlight is a perfect example of polychromatic light, as it contains all the visible wavelengths that combine to form white light. When this light interacts with the atmosphere or objects, it can be scattered or reflected to produce a range of colours.
• In a rainbow, polychromatic sunlight is dispersed through water droplets, splitting into its constituent colours across the visible spectrum, producing the familiar bands of red, orange, yellow, green, blue, indigo, and violet.
• The opposite of polychromatic is monochromatic, which refers to light composed of only one wavelength, producing a single colour or hue.

• Potential energy can be converted into other forms of energy, such as kinetic energy, which is the energy of motion.
• Potential energy is not currently being used, but it has the potential to do work in the future.
• Potential energy comes in different forms such as:
  • Chemical potential energy is the energy stored in the bonds between atoms and molecules in a substance, such as the energy stored in food.
  • Elastic potential energy is the energy stored in an object when it is compressed or stretched, such as a spring.
  • Electric potential energy is the energy stored in an electric field due to the position of charged particles, such as the energy stored in a battery.
  • Gravitational potential energy is the energy an object has due to its position in a gravitational field, such as a ball held up in the air.

• Power measures how quickly energy is used or generated.
• In physics, power is defined as the rate at which work is done or the rate at which energy is transferred or converted. It quantifies how quickly energy is used or generated within a system.
• When work is done on an object, energy is transferred to or from it, and power measures how rapidly this transfer occurs.
• Essentially, power describes the efficiency or speed of energy conversion processes.
• The equation used to measure power is P = W/t, where P is power, W is work, and t is time.
• Energy is measured in joules, while power is measured in watts or joules per second.

Here is an example:

• If you lift a 10 kg object one meter in two seconds, the work done is W = Fd = mg*d = 10 kg * 9.81 m/s^2 * 1 m = 98.1 J, where F is the force applied, d is the distance lifted, m is the mass of the object, and g is the acceleration due to gravity.
• The power used to lift the object is then P = W/t = 98.1 J / 2 s = 49.05 W.
• This means that you are transferring energy to the object at a rate of 49.05 J/s, or 49.05 watts.

• Horsepower is another unit of power where one horsepower is equal to 745.7 watts
• One horsepower is equivalent to the power required to lift 550 pounds of weight at a rate of one foot per second.
• James Watt, a Scottish engineer, adopted the term in the late 18th century to compare the output of steam engines with the power of draft horses. It was later expanded to include the output power of other types of piston engines, turbines, electric motors, and other machinery.

• Human perception of colour is based on the sensitivity of the eye to the electromagnetic spectrum, specifically the visible spectrum of light that includes spectral colours between red and violet.
• A set of primary colours is a set of coloured lights or pigments that can be combined in varying amounts to create a wide range of colours.
• Different sets of primary colours are used for additive colour mixing (of light) and subtractive colour mixing (of pigments).
• Colour models such as RGB, CMY and RYB use different sets of primary colours.
• The process of combining colours to produce other colours is used in applications such as electronic displays and colour printing to create a range of colours that can be perceived by humans.
• Additive and subtractive colour models can be used to predict how wavelengths of visible light or pigments interact with each other.
• RGB colour is a technology used to reproduce colour in ways that match human perception.
• The primary colours used in colour-spaces such as CIELAB, NCS, Adobe RGB (1998), and sRGB are determined by an extensive investigation of the relationship between visible light and human colour vision.
• An important point to note is that while there are several different sets of primary colours, there is no universally agreed upon set of primary colours. Different colour models and industries use different sets of primary colours. The specific hue that correspond with each primary colour can also vary depending on the colour model , colour space and mediums concerned.

•  A primary rainbow appears when sunlight is refracted as it enters raindrops, reflects once off the opposite interior surface, is refracted again as it escapes back into the air, and then travels towards an observer.
• The colours in a primary rainbow are always arranged with red on the outside of the bow and violet on the inside.
• The outside (red) edge of a primary rainbow forms an angle of approx. 42.4⁰ from its centre, as seen from the point of view of the observer. The inside (violet) edge forms at an angle of approx. 40.7⁰.
• To get a sense of where the centre of a rainbow might be, imagine extending the curve of a rainbow to form a circle.
• If your shadow is visible as you look at a rainbow its centre is aligned with your head.
• A primary rainbow is only visible when the altitude of the sun is less than 42.4°.
• Primary bows appear much brighter than secondary bows and so are easier to see.
• The curtain of rain on which sunlight falls is not always large enough or in the right place to produce both primary and secondary bows.

Remember that:

• The centre of a rainbow is always on an imaginary straight line (the axis of the rainbow) that starts at the centre of the Sun behind you, passes through the back of your head, out through your eyes and extends in a straight line into the distance.
• The centre-point of a rainbow is sometimes called the anti-solar point. ‘Anti’, because it is opposite the Sun with respect to the observer.
• The axis of a rainbow is an imaginary line passing through the light source, the eyes of an observer and the centre-point of the bow.
• The space between a primary and secondary rainbow is called Alexander’s band.