The Geometric Origins of Reflection, Refraction and Diffraction.

Most of us are introduced to the line as a symbol of light in the form of a ray, before we even know the geometrical meaning of a line or a ray. We are further indoctrinated in this way by way of smoke and mirrors! In darkened rooms are fantastical imaginings are guided toward one simple" truth" light rays travel in straight lines!

We dare not ask the questions that a blind man would, for we are encouraged vigorousltpy and with no small amount of coercion that thus is obvious and indeed a trivial observation.

Nothing could have been further from the truth!

The 2 fundamentals in any Spaciometry are the " point" and the " drawn line " between "points". For details of this you will have to read my many posts on the seemeioon and the gramme.

The gramme is a line with a point at the beginning and a point at the end, but we have to define an order of points to logically found the greater on the lesser., and by the higher order of points we ay define the straight line as a set of dual points within a circular "plane" of dual points which are distinguished by a collinear set of Duvall points defined relative to 2 arbitrary but fixed points in the plane. Thus a straight line is consistent of points of dual dual order?

We may construct any straight line but the finishing touch is to draw a connecting line that runs through all the dual dual order points.

Thus any straight line consists in all these drawn line segments between and passing through thepoints of the required order . The straight line, and indeed any drawn line is naturally segmented. The word segment means to "break apart". This precisely the meaning of the Latin fringere and its declensions. Thus a line is fractioned at a point.

It was common practice among the Pythagoreans to fraction a line at some distinguished point and then to rotate the 2 line segments relative to each other using this point as a centre for rotation, to form rectilineal shapes closed or open.

This fraction and rotation was applied to the representation of perception , and then gradually the representing of a ray of light. This first fraction of a line was useful,also for describing the reflection in a mirror ?

The etymology of reflection is revealing .

The word means to bend back..,thus the Romans understood that light rays were bent back at the surface of a mirror at the point of fraction of the light ray.. This bending back was a rotation of the light ray around the point of fraction. The Latin hides the plain geometric understanding of one line rotated relative to another, and introduces the complement angle or arc measure of a 2 line rotation , the circular arc is the preferred astronomical form of measure and so a bending back refers to the larger of the 2 arcs around a pair of line segment fractioned from a straight line. This is called the reflexive arc or angle from the Latin conception.

However, the light ray was also deflected from its course, and in the case of a burning mirror this deflection was measured relative to the orthogonal line to a point of fraction in a surface. This orthogonal line represents the standard relationship between an observer and his mirror image, this mirror image was defined as the reflected image, and rays that were orthogonal to a mirror surface were indistinguishable from the incident ray. But a slight deflection from this normal relation lead to a larger reflection of the ray as measured relative to the normal incident ray.

Reflection came to be measured not by the larger rotation but by the complement rotation measured from the normal. The notion of bending back was lost in this method and the notion of deflection from the normal replaces it. However we retin the term reflection giving the false notion that we know hereof we speak! In fact this represents a confusing twist in understanding we love to retin to this day!

What we have established is the relationship between the mirror and the fraction point of a line ray . This fraction point is called the point of incidence, nd now the geometrical relation to a line segment is completely obscured in terminologically sense. This require a pedagogue to decode the meaning of terms! Jobs for the Boys.

We have obscured deflection by retaining the correct rotational term reflection, and we have obscured the point of fraction with the term incidence. The geometric nature is now well mixed up!

The meaning of incident is the point where the light falls onto.
This is clearly a notion derived from empirical observation of a mirror and not from a geometrical fractioning or sectioning or segmenting or fragmenting of a line segment int 2 smaller line segments.

In the case of a burning lens or glass, or a sparkling crystal of a translucent or transparent quality, it is geometrically obvious that the line that represents a ray of light will be fractioned or segmented in at least 2 places, and potentially rotated at each point of fraction. The notion of a ray of light is empirically derived from watching sunlight streaming through holes in dense clouds, or from watching sunlight stream into dusty rooms.

There is much empirical data on the rectilineal streaming of light to found the geometrical representation as a line ray. There is also multiple empirical data for these "line rays " of light having multiple points of fraction in translucent and transparent material like glass, crystals, cut diamonds and gemstones and clear water in transparent containers. Thus it should be clear and simple to establish a definition of Refraction

Refraction is the geometrical manner in which a line ray of light propagates THROUGH a material from the point of incidence to the point of exidence. The propagation follows the scheme of fraction points thus, the first point of fraction of the line followed by a rotation of the line segment to the second point of fraction ( the refraction) of the line ray followed by a rotation of the line ray to the 3rd point of fraction( refraction) of the line ray and this is followed by a rotation. This continues until a point of fraction ( a refraction ) of the line is a point of exit or emergence from the material followed by a final rotation.

It is therefore clear that refraction is descriptive of a mode of PROPAGTION through a material, and the re alerts the observant reader to the existence of prior points of fraction and rotations..

Why is there a confusion in the concept of refraction them? Because no one has had explained to them the meaning of the word in a geometrical sense.
Even the best attempts are confused and confusing. The geometrical apprehension of these terms has been lost to many succeeding generations since they were first coined..

We now have 2 different ways in which a line ray representing a line ray of light, describes the propagation of that light ray. . The geometrical analogues meant that the laws of reflection by Ptolemy and the laws of refraction by Ibn Sahd were inevitable once the obfuscation between light as a ray and a straight line as representing the propagation of that light ray was settled. It takes time and empirical accomodation through trial and error to identify that the drawn representation captures reliably the physical and empirical data, and to establish safe manipulation and construction practices.

We now come to a modern discovery relating to the propagation of light as a ray, and the entirely new terminology of Diffraction. It is not certain that Grimaldi was the first to observe this phenomenon of light ray propagation, but it is clear that he was the first to name it.

This propagation was through a pin hole.

On the face of it there should be no point of fraction for a light ray passing entirely through a pin hole. But whereas a drawn line is straight and does not " spread" as it is drawn, a sinle pin hole light ray is always observed to Spread.

Often, in a pedagogical effort to convince students that light travels in straight lines, a philosophical and physical nonsense, educators have employed a long thin cylinder drilled out through the centre. The light ray is then demonstrated to propagate through this contraption when it has precisely a unique orientation. However this is more smoke and mirrors foisted on young gullible minds in the name of science.

Quite apart from introducing 2 points of fraction into a light ray , it completely ignores the spreading of the light rays both between the pin hole and the cylindrical entrance and the cylindrical exit and the wall or scree, . In addition the angle of the cylinder is not precisely one orientation. The observer is asked to accept this as demonstrated due to the difficulty in demonstrating it geometrically precisely! And finally the analogy says nothing about light travelling in straight lines or the parallel sides of straight cylinders, it says that a light ray may be effectively represented by a geometrical straight line,

Grimaldis's discovery lead him to a new description of how light propagated through a pin hole and a concept of the constituent nature of light, as a ray. We will study his theory of light propagation as Newyon did because it was the basis of Newtons thinking on light propagation,mand why he eventually decided the pressure propagation of light in the plenum was incorrect for light .

One has to recognise the general background of explaining invisible propagations in material. The notion of a pressure transmitted through a matrilineal at various peeps was accepted as a sound mechanical model. In fact Neeton himself using Boyles gas experimental data was ble to establish a mhnsm for the propagation of sound. So when Descatres made the rational extrapolation to light as a pressure travelling at infinite speed he was conjecturing what many would eventually come to consider.

However, because he believed in rationality( god inspired thinking) he I'd not concern himself too much with empirical data. Grimaldi on the other hand was an empiricist, and this influenced how he applied the geometrical models to explain the observed behaviours. In this he was doing hat Greek pragmatist I'd, modelling the data by analogy. Descartes on the other hand was making the data conorm to his rational model. Thus he overlooked many things because he used a test of sufficieny, and ignored what was necessary to reproduce the observed data.
This definition is almost exactly how Grimaldi defined or coined the word Diffraction. Light was not just bent or deflected it was split apart along it's longitudinal axis, that is a ray of light was split into multiple rays that spread from the pin hole with no known point of fraction!

The convention to this point was that a light ray has a point of incidence. This point of incidence is a geometrical point of fraction in the geometrical representation of the line ray. That point of fraction is a centre of rotation around which the segmented lines rotate relatively. Thus the propagation of the now deflected ray segment can be envisaged. However, in a pin hole there is no point of fraction and so no centre of rotation. One would expect the line to continue on its straight path undetected.. But the light ray clearly on careful observation shows a spreading behaviour. Now as the light ray exits the pin hole it encounters no point of incidence and so no point of refraction. Thus again there is no centre of rotation.,so again the light ray might be expected to continue in a straight line. Thus an Anomally is indicated. The light ray clearly spreads. There are no points of fraction or refraction, and so no centres of rotation to explain the deflection.


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