Rectilinear propagation and light reflection

in StemSociallast year

Gif_Propagación rectilínea de la luz.gif

Greetings to the entire academic and scientific community of


If we have been able to explore our environment it is thanks to the understanding of the phenomenon of light, said phenomenon together with that of movement are essential or vital for our existence in this so complex but kind universe, and the universe like us will always keep an intrinsic relationship with such indispensable phenomena because without them nothing would be possible, everything that satisfies our existence in one way or another are linked to these phenomena.

In this opportunity we will begin to know important aspects related to the phenomenon of the light, the way is long, but nourished of fundamental knowledge that the man has been able to acquire through the implementation of the science as his main tool for the understanding of the innumerable learnings extracted of our mother nature.

From the above, we must highlight the work of the spectacular physical science and mathematics because they have given us the clearest understanding of our surroundings, however complex it may be. On this occasion, to be able to interpret the phenomenon of light, we will be guided by the help of optics (according to its Greek origin, optós, visible) and this, without doubt, we can say that it is one of the most fertile branches of physics for all its contributions in relation to white or visible light.

In order to develop our purpose, it is impossible to leave geometry aside since it is a branch of mathematics and has accompanied us throughout our history.

Already raised the link for our purpose in search of understanding the phenomenon of light, we can express that geometric optics has impacted extraordinarily in the development of other important sciences such as astronomy and biology, this in relation to the invention of the telescope and microscope respectively, these inventions were based on the study of geometric optics and its understanding of the phenomenon of light.

If we wander through some fraction of our history we might come across the theoretical proposals made by both the Pythagoreans of ancient Greece and the Platonists, where the former suggested that our vision originated from the projection of the images emitted from objects into our eyes.

And the Platonists proposed the opposite, that is, that this vision originated due to the projection of the different rays thrown from our eyes towards the objects that were in our environment. The important thing to emphasize is that both theories served as a foundation to give origin to one of the most shocking and essential concepts within the world of optics as it is the ray.

This conceptualization of lightning was implemented by the great Euclid in order to model the path or trajectory of light, deducing that these rays managed to travel infinitely and in the form of a straight line. This proposal or approach was confirmed by Heron of Alexandria through his theory of mirrors and its practical applications, where, in the same way that Euclid estimated that the shortest trajectory to express the propagation of light was that of a straight line, this outstanding principle was taken up again by the renowned Pierre de Fermat.

We cannot leave aside the approach made by the famous Sir Isaac Newton, which consisted of a corpuscular vision of light, that is, a current or movement of particles which propagate or move with a formidable speed following a straight line, and thus structuring the corpuscular theory, Due to his theory, the great Isaac Newton tested the referred laws of reflection, proposing furthermore that refraction was due to the change of the speed of light when it changed from one medium to another, where the speed of such particles increased as the density of the medium increased, that is, that the speed of the particles turned out to be proportional to the density of the medium through which they transited.

Another important approach was made by Christiaan Huygens, who considers light as a wave, and with this the wave model was born, ending this brief but important journey with the electromagnetic theory of James Clerk Maxwell who showed that light was able to travel through the vacuum.

The optics

It is important to have clear that starting from the interaction of light with each material object around us is that the optic needs to be studied, and it is made up of three parts, among which we have:

1.- Geometrical optics

Starting from a geometrical model, this part of the optics, also based on the fundamental concept of the ray, studies and establishes the route, path or trajectory of the light.

2.- Physical optics

This branch considers the wave nature of the light phenomenon, i.e. as an electromagnetic wave, and therefore explains the phenomena of interference, diffraction and polarization of light.

3.- Quantum optics

When light is related to matter at atomic levels we can say that this part of optics intervenes for the due analysis of such interaction.

For the beginning of our already mentioned purpose we will know in a general way the geometric optics and everything that relates it to the study of the light phenomenon.

Geometric optics

Geometrical optics, as we said before, implements an approximate geometrical or mathematical model in relation to the representation and propagation of light in a rectilinear way, this is done starting from luminous rays, besides this part of the optics also includes the essential phenomena of reflection and refraction of light from a macroscopic vision, so it is very important before getting to the description of such phenomena to be able to know some fundamental concepts like the ones we have below:

Light beam

It is important to take into account that when we refer to a ray of light it is because we are talking about an idealization related to a light emission, therefore, we could say that it is an imaginary line with which we represent the path or the trajectory through which the light must propagate, which it does by following a straight line as long as this is not affected by the interaction of a certain object belonging to its closest environment, since if this happens it will change its trajectory depending on the material of the object that obstructs the path of the light rays.

Optical system

It is represented by a certain set of surfaces which separate various media through which light is propagated. These optical systems are generally flat or spherical surfaces whose center is aligned along an axis which we call the optical axis of the system.

Propagation of light

For its propagation this phenomenon does not necessarily require a material support, since it can be propagated by the vacuum, in a homogeneous and isotropic material system the light will be propagated in straight line, being this last one a means whose properties are similar in any sense or orientation that is taken, and as examples we can mention means like the air, the vacuum, water, glasses, among others, the certain thing is that the light will always be propagated in straight line, in any direction and at great speed.

Next we will make a small but significant practical experience with the purpose of observing the rectilinear propagation of the light, therefore we have the following images:

Practical experience rectilinear light propagation





Through each one of the previous images, we could observe how the light propagates in a straight line, and in addition it is possible to be visualized as the luminous rays components of the light beam emitted by the lantern are concentrated in a focus or focal point of reflective material and soon they leave this focus projecting the circular form that this particular lantern has.

We can also visualize another example of our reality with respect to the rectilinear propagation of light as the one we will show in the following figure 1:

Figure 1. Another example in our environment of the rectilinear propagation of light


Speed of Light

According to the theory of relativity this speed in a vacuum represents a universal constant (c) and as we know in the physical world this constitutes the highest possible speed, the theoretical basis for which is linked to the approach to the time required for light to pass in a vacuum from one point to another.

During the nineteenth century, implementing a method based on a type of rotating mirror Foucault managed to establish a very accurate measurement of this speed, then Michelson refining the method used by Foucault was able to obtain greater accuracy, however, for the twentieth century were achieved new measurements and, currently the value for this speed of light in the vacuum is 299,792,458 m / s, which can often be rounded to 300,000,000 m / s or 300,000 km /s.

Refractive Index (n)

If we have that in a certain material medium the speed of light is (v), having always clear that said speed (v) must be less than (c), so we call the absolute refractive index of a certain medium the quotient between the universal constant c (which represents the speed of light in a vacuum) and the speed determined in that particular medium (v), therefore we have the following equation or mathematical formulation:

Fórmula 1.png

Then in (1) we observe that the magnitude of the absolute refractive index is dimensionless because it relates to two types of velocities, where their units cancel each other out, and its value will always be greater than the unit, this because it is c>v. In a given medium with homogeneous and isotropic characteristics, this absolute refractive index would be constant.

Fermat's Principle

We already knew the absolute refractive index (n), which is necessary to consolidate Fermat's important principle, which states that the product between the refractive index and the path that light travels or travels in a given homogeneous medium determines what is known as the optical path of this luminous phenomenon, therefore, we can establish the following equation:

Fórmula 2.png

Light reflection

If we find that a beam of light arrives or crashes on a surface that separates two homogeneous media, and it changes its direction but without changing its initial means of propagation, we can then express that it has been reflected, for example, when a certain object reflects a light and this crashes against a flat mirror will change its direction but we will visualize behind this mirror an image, as we will see in the following figure 2.

Figure 2. Light reflection in a flat mirror


It is important to emphasize that depending on the surface that interacts with certain rays of light we can establish two types of reflections, one called specular (like the one in our previous example), and the other reflection that we would find is the diffuse one, and this contrary to the first one is related to surfaces that present irregularities either macroscopically or microscopically, in the second case we would see that the light would be deviated in fortuitous directions.

In order to specify the geometric shape of the light reflection in terms of a smooth surface, we must specify the following elements:

a) Incident ray: it is the one that affects the limit of the means involved.

b) Reflected lightning: is the lightning that returns through the initial means of propagation when it hits the border.

c) The normal one: this represents the straight line which is perpendicular to the surface where the lightning strikes or impacts.

(d) Angle of incidence: This angle is formed by the ray incident on the surface, i.e. the ray incident with the line perpendicular or normal to that surface.

e) Angle of reflection: This angle is formed by the ray reflected from the surface and the straight line normal to the surface. The above described can be seen in the following figure 3.

Figure 3. Specular light reflection


And complementing the information expressed in the previous figure we can continue with the laws of light reflection which express the following:

1.- In the so-called plane of incidence there are both the incident beam and the normal or perpendicular line to that refracting surface, as well as the beam reflected from the same surface described above, i.e. these elements are in the same plane.

2.- Both the angle formed by the incident beam (i) and the angle formed by the reflected beam (i') are equal.

A long way to go in understanding the essential phenomenon of light, the important thing is to be able to go step by step for a better analysis of such a vital phenomenon for all of us.


Through our extraordinary and essential senses we are reliable witnesses of the majesty of our universe, and together with science we have been able to interpret essential phenomena that have allowed us to increase our intellect and comfort in each of the spaces related to our activities. In this way we can express that the perception that each of us has of our environment is mainly due to the understanding of the phenomena of light.

In the development of this article we were able to highlight important conceptual aspects very useful for the understanding of geometric optics, among which were the light ray, optical system, light propagation, speed of light, refractive index, describing also Fermat's essential principle which proposes that the product between the absolute refractive index (n) and the path travelled by light (s) in a homogeneous medium constitutes the optical path of the mentioned luminous phenomenon.

When the luminous rays that make up a beam of light move through space, they can encounter different obstacles, which leads to other types of intrinsic phenomena such as the reflection of light. In terms of reflection, depending on the surface of the obstacle, it can be considered either specular or diffuse reflection, the example given in this article was the specular one in figure 2.

To close we must highlight the development of a small but important practical experience where we were able to demonstrate the rectilinear propagation of light and also knew another example of our daily life as observed in Figure 1.

Until another delivery my appreciated readers of, especially to the members of the community of #stemsocial, for which I recommend widely to be part of this wonderful project, since it allows us to value the great task of the academy and the great effort of the scientific field.

Note: All images were made using the Power Point application, and the animated gif was made with the PhotoScape application.

Bibliographic References

[1]Charles H. Lehmann. Geometría analítica


[3] Development of Geometric Optics



Good work! Thanks for sharing.

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Excellent way to highlight the importance of geometry and optics of light behavior, thanks for sharing. Greetings.

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