Laws of reflection

About the laws of reflection

When light reflects off a surface or object it always behaves predictably and according to three rules (or laws).

  • The three laws of reflection are:
    • The incident ray, the reflected ray and the normal to a surface all lie on the same plane.
    • The angle of the incident ray is equal to the angle which the reflected ray makes with the normal.
    • The incident ray and the reflected ray appear on opposite sides of the normal.

Lines that are normal to one another

About lines that are normal to one another
  • If one line is normal to another, then it is at right angles.
  • In geometry, a normal (or the normal) refers to a line drawn perpendicular to and intersecting another line, plane or surface.
  • In the field of optics, the normal is a line drawn on a ray diagram perpendicular to (at 900 to), the boundary between two media.
  • If the boundary between two media is curved then the normal is drawn at a tangent to the boundary.

Neuron anatomy

About the anatomy of neurons
  • A typical neuron consists of a cell body (soma), dendrites, and a single axon.
  • Dendrites and axons form filament-like extensions of the soma.
  • Dendrites typically form into a profusion of branches as they extend from the soma.
  • An axon can be as long as a metre in length.
  • At the farthest tip of the axon’s branches are axon terminals, where the neuron can transmit a signal across a synapse to another cell.

lateral geniculate nucleus

Lateral geniculate nucleus

The lateral geniculate nucleus is a relay centre on the visual pathway from the eyeball to the brain. It receives sensory input from the retina via the axons of ganglion cells.

The thalamus which houses the lateral geniculate nucleus is a small structure within the brain, located just above the brain stem between the cerebral cortex and the midbrain with extensive nerve connections to both.

The lateral geniculate nucleus is the central connection for the optic nerve to the occipital lobe of the brain, particularly the primary visual cortex.

Both the left and right hemispheres of the brain have a lateral geniculate nucleus.

There are three major cell types in the lateral geniculate nucleus which connect to three distinct types of ganglion cells:

  • P ganglion cells send axons to the parvocellular layer of the lateral geniculate nucleus.
  • M ganglion cells send axons to the magnocellular layer.
  • K ganglion cells send axons to a koniocellular layer.

The lateral geniculate nucleus specialises in calculations based on the information it receives from both the eyes and from the brain. Calculations include resolving temporal and spatial correlations between different inputs. This means that things can be organised in terms of the sequence of events over time and the spatial relationship of things within the overall field of view.

Some of the correlations deal with signals received from one eye but not the other. Some deal with the left and right semi-fields of view captured by both eyes. As a result, they help to produce a three-dimensional representation of the field of view of an observer.

  • The outputs of the lateral geniculate nucleus serve several functions. Some are directed towards the eyes, others are directed towards the brain.
  • A signal is provided to control the vergence of the two eyes so they converge at the principal plane of interest in object-space at any particular moment.
  • Computations within the lateral geniculate nucleus determine the position of every major element in object-space relative to the observer. The motion of the eyes enables a larger stereoscopic mapping of the visual field to be achieved.
  • A tag is provided for each major element in the central field of view of object-space. The accumulated tags are attached to the features in the merged visual fields and are forwarded to the primary visual cortex.
  • Another tag is provided for each major element in the visual field describing the velocity of the major elements based on changes in position over time. The velocity tags (particularly those associated with the peripheral field of view) are also used to determine the direction the organism is moving relative to object-space.

Optic chiasm

Optic chiasm

The optic chiasm is the part of the brain where the optic nerves partially cross. It is located at the bottom of the brain immediately below the hypothalamus.

The cross-over of optic nerve fibres at the optic chiasm allows the visual cortex to receive the same hemispheric visual field from both eyes. Superimposing and processing these monocular visual signals allows the visual cortex to generate binocular and stereoscopic vision.

So, the right visual cortex receives the temporal visual field of the left eye, and the nasal visual field of the right eye, which results in the right visual cortex producing a binocular image of the left hemispheric visual field. The net result of optic nerves crossing over at the optic chiasm is for the right cerebral hemisphere to sense and process left-hemispheric vision, and for the left cerebral hemisphere to sense and process right-hemispheric vision.


Optic nerve

Optic nerve

The optic nerve is the cable–like grouping of nerve fibres formed from the axons of ganglion cells that transmit visual information towards the lateral geniculate nucleus.

The optic nerve contains around a million fibres and transports the continuous stream of data that arrives from rods, cones and interneurons (bipolar, amacrine cells). The optic nerve is a parallel communication cable that enables every fibre to represent distinct information about the presence of light in each region of the visual field.

Müller cells

Müller cells

Müller glia, or Müller cells, are a type of retinal cell that serve as support cells for neurons, as other types of glial cells do.

An important role of Müller cells is to funnel light to the rod and cone photoreceptors from the outer surface of the retina to where the photoreceptors are located.

Other functions include maintaining the structural and functional stability of retinal cells. They regulate the extracellular environment, remove debris, provide electrical insulation of the photoreceptors and other neurons, and mechanical support for the fabric of the retina.

  • All glial cells (or simply glia), are non-neuronal cells in the central nervous system (brain and spinal cord) and the peripheral nervous system.
  • Müller cells are the most common type of glial cell found in the retina. While their cell bodies are located in the inner nuclear layer of the retina, they span the entire retina.


Neurons are the cells that transmit electrical impulses around the brain and the other parts of the central nervous system.

  • Neurons are the electrically excitable cells that form the central nervous system of human beings.
  • Neurons interconnect the systems and organs that maintain the body’s essential functions.
  • Neurons send and receive signals that allow us to sense the external world, move, think, form memories and much more.
  • Neurons are of three principal types: motor neurons, sensory neurons and interneurons.
  • Neurons connect together via specialized filaments called synapses.
  • In the neocortex (making up about 80% of the human brain), approximately 70-80% of nervous tissue is in the form of neurons whilst the remainder is composed of interneurons.
About the anatomy of neurons
  • A typical neuron consists of a cell body (soma), dendrites, and a single axon.
  • Dendrites and axons form filament-like extensions of the soma.
  • Dendrites typically form into a profusion of branches as they extend from the soma.
  • An axon can be as long as a metre in length.
  • At the farthest tip of the axon’s branches are axon terminals, where the neuron can transmit a signal across a synapse to another cell.
About interneurons
  • Interneurons are also referred to as relay neurons, connector neurons, intermediate neurons and local circuit neurons each of which helps to explain their function.
  • Interneurons form nodes within neural circuits, enabling communication between sensory or motor neurons and the central nervous system.
  • Interneurons can be further broken down into two groups: local interneurons and relay interneurons.
    • Local interneurons have short axons and form circuits with nearby neurons to analyse small pieces of information.
    • Relay interneurons have long axons and connect circuits of neurons in one region of the brain with those in other regions.
  • The interaction between interneurons allows the brain to perform complex functions such as sense-making.
About neurons and the human retina

Microscopic images of the Sun

When an observer looks up into the sky and sees an atmospheric rainbow they are looking at tiny images of the Sun mirrored in millions of individual raindrops. This is what produces the impression of arching bands of colour.

  • It is the mirror-like surfaces on the inside of raindrops that reflect microscopic images of the Sun towards an observer.
  • The images are tiny because raindrops are small, but also because the surface they reflect off is concave.
  • At a micro-scale, each image of the Sun is different:
    • Each and every image is a different colour and depends on the wavelength of light each raindrop is reflecting towards an observer’s eyes at any particular moment.
    • For convenience sake, wavelength is usually measured in nanometres, but nanometres can be divided into picometres (or even smaller units). This means that an observer is looking at countless wavelengths of light and so countless colours.
    • The images range in size and shape depending on the dimensions of the droplets and turbulence in the atmosphere. The size and roundness of raindrops also affect the appearance of a rainbow as a whole.
  • The millions of microscopic images of the Sun that produce the impression of a rainbow is similar to the way pixels of light produce the images we see on digital displays.
Notice that:
  • If all the rays of incident light that contribute to the formation of an observer’s rainbow are traced back from each raindrop towards the Sun it transpires that they are produced by parallel rays and that each incident ray is polarized as it passes through a droplet.
  • If all the rays of incident light that travel through a single raindrop as it falls are compared, it transpires that they are all parallel with the axis of the rainbow.

Observer’s point of view

To understand rainbows it is important to sort out what an observer is actually looking at.

  • Rainbows only exist in the eyes of an observer.
  • Every observer sees a different rainbow produces by a unique set of raindrops that happen to be in the right place at the right time.
  • The individual raindrops that result in the appearance of a rainbow for one observer are always different from the raindrops that produce a rainbow for someone else.
  • As an observer moves, their rainbow moves with them. Seen from a car window, the rainbow appears stationary whilst the landscape rushes past.
From an observer’s point of view
  • Atmospheric rainbows appear to an observer as arcs of colour across the sky. From an aeroplane, a rainbow can appear as entire circles of colour.
  • Even from the ground, it is easy to deduce that every rainbow has a centre point around which the arcs of a rainbow are arranged.
  • The exact position in the sky where an atmospheric rainbow will appear can be anticipated by working out where its centre will be.
  • The centre of a rainbow is always on an imaginary straight line 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 eyes of an observer are always aligned with the rainbow axis.
  • To an observer, the rainbow axis appears as a point, not a line, and that imaginary point marks the centre of where every rainbow will appear.
  • The idea that a rainbow has a centre corresponds with what an observer sees in real-life.
  • The idea of a rainbow axis or anti-solar point corresponds with a diagrammatic view showing the scene in side elevation.
Looking for rainbows
  • To work out where a rainbow might appear:
    • Turn your back on the Sun.
    • If you can see your shadow, look at the head. The axis of the rainbow runs from the Sun behind you, through your eyes and through the head of your shadow. Imagine where your eyes might be in your shadow. If a rainbow appears that point will be its centre.
    • If you can’t see your shadow, just try and imagine the line from the Sun, passing through your head and then extend it away from you till it reaches the landscape. At whatever point it touches, that will be the centre.
    • Unless you are in a plane, the centre point is always below the horizon so on the ground or in the landscape in front of you.
    • Now, with the Sun behind you spread out your arms to either side or up and down at 450 from the centre point.
    • Swing them round like the blades of a windmill. That is where your primary rainbow will appear.
Remember that:
  • Every observer has a rainbow axis and a centre-point on that axis that moves with them as they change position. It means that their rainbow moves too.
  • The centre of a secondary rainbow is always on the same axis as the primary bow and shares the same anti-solar point.
  • To see a secondary rainbow look for the primary bow first – it has red on the outside. The secondary bow will be a bit larger with violet on the outside and red on the inside.
Rainbows as discs of colour
  • Close consideration of why rainbows appear as arcs or circles can be explained by the idea that an observer is looking at superimposed, concentric discs of colour.
  • Think in terms of each observed band of colour within a rainbow forming on the edge of a separate coloured disc.
  • The area close to the circumference of each disc produces the most intense and brilliant colour.
  • The intensity of each colour drops sharply away from the circumference of its disc and towards the centre.
  • The observed colour of each disc corresponds with the band of wavelengths that produces it.
  • The fact that we see distinct bands of colour in a rainbow is often described as an artefact of human vision.
  • Each disc contributes small amounts of its own colour to the area towards the shared centre of the six concentric discs making the sky appear lighter.

Minimum angle of deviation

The minimum angle of deviation of a ray of light of any specific wavelength passing through a raindrop is the smallest angle to which it must change course before it becomes visible within the arcs of a rainbow to an observer.

  • Any ray of light (stream of photons) travelling through empty space, unaffected by gravitational forces, travels in a straight line forever.
  • When light travels from a vacuum or from one transparent medium into another, it deviates from its original path (and changes speed).
  • The more a ray changes direction the greater its angle of deviation.
  • A ray reflected directly back on itself has an angle of deviation of 1800 – the maximum possible angle of deviation.
  • It is the optical properties of air and raindrops that determines the angle of deviation of any ray of incident light.
  • It is the optical properties of raindrops that prevent any ray of visible light within the visible spectrum from exiting a raindrop towards an observer at an angle of deviation less than 137.60.
  • The angle of deviation and the angle of deflection are directly related to one another and together always add up to 1800.
  • The angle of deviation and the viewing angle are always the same.
More about the minimum angle of deviation
  • The optical properties of an idealised spherical raindrop mean that no light of any particular wavelength can deviate at less than its minimum angle of deviation.
  • The minimum angle of deviation of visible light depends on its wavelength.
  • The minimum angle of deviation for red light with a wavelength of approx. 720 nm is 137.60 but similar rays of the same wavelength but with other impact parameters can deviate up to a maximum of 1800.
  • Different colours have different minimum angles of deviation because the refractive index of water changes with wavelength.
Impact parameter and minimum angle of deviation
  • To form a primary rainbow, incident light must strike each raindrop above its horizontal axis.
  • Rays of incident light of a single wavelength strike a raindrop at every possible point on the side of a raindrop facing the Sun.
  • Only those that strike above the horizontal axis contribute to a primary rainbow.
  • Points of impact of incident light striking a droplet can be measured on an impact parameter scale.
  • It is the point of impact of rays of incident light of the same wavelength that is the variable factor that determines their subsequently different paths.
  • Rays that strike nearest the horizontal axis, so with a value near 0.0 on an impact parameter scale have the largest angles of deviation.
  • Rays that strike farthest away from the horizontal axis (near the topmost point on an impact parameter scale and so near 1.0) also have a large angle of deviation.

Laws of refraction and reflection

The path of light through a raindrop is a key factor in determining whether it will direct light towards an observer and contribute to their perception of a rainbow. This can be broken down as follows:

  • The impact parameter is a measure of the direction from which rays of incident light approach a raindrop and the point at which they strike the surface.
  • When using a ray-tracing diagram to map the path of rays through a raindrop, an impact parameter scale is used to select which incident rays are of interest.
  • An impact parameter scale is aligned with parallel incident rays and divides the relevant part of the surface of a droplet into equal parts.
  • Using a scale with steps between zero and one, 0 is aligned with the ray that passes through the centre of a droplet and 1 with the ray that grazes the surface without refraction or reflection.
Remember that:
  • Primary rainbows form when incident light strikes raindrops above their horizontal axis reflecting once off the inside before exiting towards an observer.
  • Incident light that strikes raindrops below their horizontal axis and reflects once on the inside before exiting, directs light upwards away from an observer.
  • Secondary rainbows form when incident light strikes raindrops below their horizontal axis reflecting twice off the inside before exiting downwards.
  • The Law of reflection deals with the angles of incidence and reflection when light strikes and bounces back off a surface and can be used for calculations relating to the curved surfaces of a raindrop.
  • Remember that the law of reflection states that the angle of incidence always equals the angle of reflection for a mirror-like (specular) surface.
  • The Law of Refraction (Snell’s law) deals with the changes in the speed and direction of incident light as it crosses the boundaries between air and a raindrop and then between a raindrop and the surrounding air.
  • An equation can be derived from Snell’s law that deals with the relationship between the angle of incidence and the angle of refraction of light with reference to the refractive indices of both media.

Light sources for rainbows

The best light source for a rainbow is a strong point source such as sunlight. Sunlight is ideal because it is so intense and contains all the wavelengths that make up the visible spectrum.

  • A human observer with binocular vision (two eyes) has a 1200 field of view from side to side. In clear conditions, the Sun can be considered to be a point-source filling just 0.50 of their horizontal field of view.
  • A wide range of visible wavelengths of light is needed to produce all the rainbow colours. The Sun produces a continuous range of wavelengths across the entire visible spectrum.
  • When atmospheric conditions like cloud or fog cause too much diffusion of sunlight before it strikes a curtain of rain, no bow is formed.
  • Artificial light sources such as LED’s, incandescent light bulbs, fluorescent lights and halogen lamps all make poor light sources because they emit too narrow a range of wavelengths and don’t emit sufficient energy.

Looking closely at rainbows

There are several particularly noticeable things to see when looking closely at rainbows:

  • The arcs of spectral colours curving across the sky with red on the outside and violet on the inside, this is a primary rainbow. The arcs appear between the angles of approx. 40.7° and 42.4° from the centre (anti-solar point) as seen from the point of view of an observer.
  • There may be another rainbow, just outside the primary bow with violet on the outside and red on the inside, this is the secondary rainbow. The arcs appear between the angles of approx. 50.4° and 53.4° from its centre as seen from the point of view of an observer.
  • Faint supernumerary bows often appear just inside a primary rainbow and form shimmering arcs of purples and cyan-greens. These bands appear at an angle of approx. 39° to 40° from the centre so just inside the violet arc of the primary bow.
  • The remaining area inside a rainbow from its centre out to approx. 39° often appears lighter or brighter in comparison to the sky outside the rainbow. There are three main causes:
    • Light strikes multiple droplets in succession and randomly scatters in all directions.
    • Small amounts of light of all wavelengths are deflected towards the centre and combine to produce the appearance of weak white light.
    • Almost no light is deflected to the area outside a rainbow.
  • When a secondary rainbow appears, the area between the two often appears to be darker in tone than any other area of the sky. This is called Alexander’s band. The effect is the result of rays being deflected away from this area as primary and secondary bows form.

Looking for rainbows

The weather, season and time of day are all important if you hope to see an atmospheric rainbow.

  • The best rainbows appear in the morning and evening when the Sun is strong but low in the sky.
  • Northern and southern latitudes away from the equator are good for rainbows because the Sun is lower at its zenith.
  • Mountains and coastal areas can create ideal conditions because as air sweeps over them, it cools, condenses and falls as rain.
  • Rainbows are rare in areas with little or no rainfall such as dry, desert conditions with few clouds.
  • Too much cloud is not good because it blocks direct sunlight.
  • Winter is not necessarily the best season because the light is weaker and there can be excessive cloud.
  • Rainbows are less common around midday because the higher the Sun is in the sky the lower the rainbow.
  • If the Sun is too high, then by the time the raindrops are in the right position to form part of a rainbow they are lost in the landscape.

Orders of rainbows

Primary rainbows are sometimes referred to as first-order bows. First-order rainbows are produced when light is reflected once as it passes through the interior of each raindrop.

Secondary rainbows are second-order bows. Second-order bows are produced when light is reflected twice as it passes through the interior of each raindrop.

  • Each subsequent order of rainbows involves an additional reflection inside raindrops.
  • Higher-order bows get progressively fainter because photons escape droplets after the final reflection. As a result, insufficient light reaches an observer to trigger a visual response.
  • Each higher-order of bow gets progressively broader spreading photons more widely and reducing their brightness further.
  • Only first and second-order bows are generally visible to an observer but multi-exposure photography can be used to capture them.
  • Different orders of rainbows don’t appear in a simple sequence in the sky.
  • First, second, fifth and sixth-order bows all share the same anti-solar point.
  • Zero, third and fourth-order bows are all centred on the Sun and appear as circles of colour around it.

Light wave

Light waves are the result of vibrations between an electric field and a magnetic field. In other words, electromagnetic waves waves are composed of oscillating magnetic and electric fields.

optical density

Optical density is a measurement of the degree to which a refractive medium slows the transmission of light.

  • The optical density of a medium is not the same as its physical density.
  • The more optically dense a medium, the slower light travels through it.
  • The less optically dense (or rare) a material is, the faster light travels through it.
  • A vacuum has the least optical density and so light travels through it at a maximum speed of 299,792 kilometres per second.
  • Optical density accounts for the variation in refractive indices of different media.


A human observer is a person who engages in observation by watching things.