Although somewhat different in its modern form, Huygens' basic concept is still very useful to us in predicting and interpreting the behavior of light. Let us recall a familiar characteristic of water waves as an introduction to this important principle. If a stone is dropped into a pool of quiet water, it creates a disturbance in the water and a series of concentric waves travels out from the disturbance point. The stone quickly comes to rest on the bottom of the pool, so its action on the water is of short duration.
However, wave disturbances persist for a considerable time thereafter and cannot reasonably be attributed to any activity on the part of the stone. It must be that the disturbances existing at all points along the wave fronts at one instant of time generate those in existence at the next instant. Huygens recognized this logical deduction as a basic aspect of wave behavior and devised a geometric method of finding new wave fronts. His concept, published in and now recognized as Huygens' principle, may be stated as follows : Each point on a wave front may be regarded as a new source of disturbance.
According to this principle, a wave front originating at a source S in Figure A arrives at the position AB. Each point in this wave front may be considered as a secondary source sending out wavelets.
Thus from points 1, 2, 3, etc. After a time t these wavelets have a radius equal to vt, where v is the velocity of the wave. The principle further states that the surface A'B' , tangent to all the wavelets, constitutes the new wave front.
It is apparent from Figure that spherical wave fronts are propagated from spherical wavelets and planar wave fronts from planar wavelets. The wave theory treats light as a train of waves having wave fronts perpendicular to the paths of the light rays. In contrast to the particle model discussed earlier, the light energy is considered to be distributed uniformly over the advancing wave front.
Huygens thought of a ray merely as a line of direction of waves propagated from a light source. The supporters of the wave theory were able to satisfactorily explain reflection and refraction of light. The explanation of refraction required that the speed of light in optically dense media, such as water and glass, be lower than the speed of light in air.
They had trouble, however, explaining rectilinear propagation. This was the primary reason Newton rejected the wave theory. Before the nineteenth century, interference of light was unknown and the speed of light in such media as water and glass had not been measured. Diffraction fringes or shadows had been observed as early as the seventeenth century. In the absence of knowledge of interference, however, neither Newton nor Huygens attached much significance to this diffraction phenomenon.
In the interference of light was discovered. This was followed in by the explanation of diffraction based on interference principles, as discussed in Chapter These two phenomena imply a wave character and cannot be satisfactorily explained by the behavior of particles. Thus despite the great prestige of Sir Isaac Newton, the corpuscular theory was largely abandoned in favor of the wave theory. The final blow to the corpuscular theory came when Foucault found that the speed of light in water was lower than the speed of light in air.
Through the remainder of the nineteenth century the wave concept supplied the basic laws from which came remarkable advances in optical theory and technology. If the temperature is high enough, these objects radiate light as well as heat.
If a light source is blocked off from an observer, its heating effect is cut off as well. For this reason, a cloud that obscures the sun's light cuts off some of the sun's heat at the same time.
The English physicist Michael Faraday became concerned with the transfer of another kind of energy while investigating the attraction and repulsion of electrically charged bodies. In these experiments led him to the principle of the electric generator. The corpuscular theory was largely abandoned in favor of the wave theory following the discovery of interference and diffraction of light.
Note that the speed of light in water had not yet been measured. Faraday's practical mind required a model to interpret and explain physical phenomena. It was difficult for him to visualize electrically charged objects attracting or repelling each other at some distance with nothing taking place in the intervening space.
Thus he conceived a space under stress and visualized tubes of force between charged bodies. Faraday was not an astute mathematician and so did not put his model for this "transmission of electric force" into abstract mathematical form. The Scottish mathematical physicist James Clerk Maxwell set out to determine the properties of a medium that would transmit the energies of heat, light, and electricity.
By the year he had developed a series of mathematical equations from which he predicted that all three are propagated in free space at the speed of light as electromagnetic disturbances. This unification, the electromagnetic theory, brought into common focus the various phenomena of radiation. Maxwell determined that the energy of an electromagnetic wave is equally divided between an electric field and a magnetic field, each perpendicular to the other, and both perpendicular to the direction of propagation of the wave.
In Section In this sense, an electromagnetic waves is a periodic disturbance involving electric and magnetic forces. A model of an electromagnetic wave at a given instant is shown in Figure By experimental confirmation of the electromagnetic theory was achieved by the German physicist Heinrich Rudolf Hertz Hertz showed that light transmissions and electrically generated waves are of the same nature.
Of course, many of their properties are quite different because of great differences in frequency. Maxwell's theory of electromagnetic waves seemed to provide the final architecture for optical theory; all known optical effects could now be fully explained. Many physicists felt at this time that all the significant laws of physics had been discovered and that there was little left to do other than develop new and more sophisticated techniques for measuring everything more accurately.
In this connection Hertz stated, "The wave theory of light is, from the point of view of human beings, a certainty. Today, the electromagnetic spectrum is known to consist of a tremendous range of radiation frequencies extending from about 10 hz to more than 10 25 hz.
All electromagnetic radiations travel in free space with the constant velocity of 3 x 10 8 meters per second. From the wave equation of Section Therefore, the range of the electromagnetic spectrum in terms of radiation wavelengths is from about 3 x 10 7 meters in the low-frequency region to less than 3 x 10 meter in the high-frequency region. In terms of the angstrom A , a unit frequently used to express the wavelengths of electromagnetic radiations, the range is from about 3 x 10 17 A to 3 x 10 -7 A, an angstrom being equal to 10 meter.
Eight major regions of the electromagnetic spectrum are commonly recognized. These regions are based on the general character of the radiations. All kinds of electronic transmissions are accommodated in the radio-wave region. Commercial electricity falls within the power region. Observe the very small region occupied by the visible spectrum. The optical spectrum includes those radiations, commonly referred to as light, that can be detected visually.
Their wave lengths range from approximately A to A. Accordingly, light may be defined as radiant energy that a human observer can see. The optical spectrum also extends into the near infrared and into the near ultraviolet. Although our eyes cannot see these radiations, they can be detected by means of photographic film. While studying the radiation characteristics of oscillatory discharges he observed that a spark discharge occurred more readily between two charged spheres when they were illuminated by another spark discharge.
At about the same time, other investigators found that negatively charged zinc plates lost their charge when illuminated by the ultraviolet radiations from an arc lamp. Positively charged plates were not discharged when similarly illuminated. Observations of the peculiar effects of ultraviolet radiation on metal surfaces led to the discovery of the photoelectric effect, a phenomenon that defied explanation based on the electromagnetic wave theory of light. Figure shows two freshly polished zinc plates A and B that are sealed in an evacuated tube having a quartz window and are connected externally to a battery and galvanometer a sensitive current-indicating meter.
The quartz window transmits ultraviolet radiation, which does riot pass through glass. The galvanometer indicates a small current in the circuit when ultraviolet light falls on the negative plate A. If a sensitive electrometer circuit is substituted for the battery, it may be shown that the plate exposed to the ultraviolet light acquires a positive charge.
The results of these experiments imply that the action of the light on the zinc plate causes it to lose electrons. The German physicist Philipp Lenard published the results of the first quantitative studies of the photoelectric phenomenon in By measuring the charge to mass ratio of the negative electricity derived from an aluminum plate illuminated by ultraviolet light, he was able to prove that electrons were ejected from the metal surface.
Such electrons are called photoelectrons. Subsequent investigations have shown that all substances exhibit photoemission of electrons. The emission of electrons by a substance when illuminated by electromagnetic radiation is known as the photoelectric effect. If the positive potential is increased enough, all photoelectrons are collected by plate B and the photoelectric current reaches a certain limiting, or saturation, magnitude.
Curve a of Figure is a graph of photoelectric current as a function of collector plate potential for a given source of light. Curve b shows the result of doubling the intensity of the light. Observe that the magnitude of the saturation current is doubled. This means, of course, that the rate of emission of photoelectrons is doubled.
Here we have evidence of the first law of photoelectric emission : The rate of emission of photoelectrons is directly proportional to the intensity of the incident light.
For an electron to escape through the surface of a metal, work must be done against the forces that bind it within the surface. This work is known as the work function. The photoelectrons must acquire from the incident light radiation the energy needed to overcome this surface barrier.
If electrons acquire less energy than the work function of the metal, they cannot be ejected. On the other hand, if they acquire more energy than is required to pass through the surface, the excess appears as kinetic energy and consequently as velocity of the photoelectrons. We may assume that light penetrates a few atom layers into the metal and that the photoelectric effect will occur at varying depths beneath the surface.
Photoelectrons ejected from atom layers below the surface will lose energy through collisions in reaching the surface and must then give up energy equal to the work function of the metal in escaping through the surface.
Photoelectrons ejected from the surface layer of atoms lose only the energy necessary to overcome the surface attractions. Thus in any photoelectric phenomenon we should expect photoelectrons to be emitted at various velocities ranging up to a maximum value possessed by electrons having their origin in the surface layer of atoms. We can test the logic of these deductions by experimenting further with the photoelectric cell of Figure A positive potential of a few volts on the collector plate B produces a saturation current as shown in Figure If the collector plate potential is lowered towards zero, the photoelectric current decreases slightly, but at zero potential may still be close to the saturation magnitude.
As the collector plate potential is made slightly negative with respect to the emitter, the photoelectric current decreases also.
By increasing this negative potential a value is reached where the photoelectric current drops to zero. This is called the stopping, or cutoff potential V , and is shown in Figure A negative potential on the collector plate repels the photoelectrons, tending to turn them back to the emitter plate.
Only those electrons having enough kinetic energy and velocity to overcome this repulsion reach the collector. As the cutoff potential is approached, only those photoelectrons with the highest velocity reach the collector. These are the electrons with the maximum kinetic energy that are emitted from the surface layer of the metal.
At the cutoff potential even these electrons are repelled and turned back to the emitter. Thus the negative collector potentials, which repel rather than attract photoelectrons, reveal something about the kinetic energy distribution of the ejected electrons. As this potential is made more negative, a nearly linear decrease in photoelectron current shows us that the photoelectrons do have a variety of velocities.
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. 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:.
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. This branch considers the wave nature of the light phenomenon, i.
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.
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:.
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.
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. 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:. 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 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.
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:.
In a given medium with homogeneous and isotropic characteristics, this absolute refractive index would be constant. 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:.
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. 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.
As a result, you could not see the source of light once you bent the tube. This very principle also helps in the formation of shadows when you hold an object in the path between the light source and a wall. However, you have to use an opaque object instead of transparent or translucent material. An opaque object refers to a material that prevents light from passing through it. For instance, light cannot even pass through a book or a cricket bat.
On the other hand, light easily makes its way in a straight line through glass or a thin piece of cloth. In this case, you can refer to these articles as transparent and translucent, respectively. For your better understanding of this interesting concept, let us give two examples of rectilinear propagation of light that take place in real life. Eclipse — Eclipse is a phenomenon when a celestial body such as Earth comes in the path of light originating from the sun and reaching the moon.
In the case of a lunar eclipse, you can see the shadow of our planet on the moon. The light is being refracted by the water, so our eyes see the pencil in two different mediums. Answer: electromagnetic light ; refraction Make 3 sets of slits with a razor in a sheet of aluminum foil like diagram. Put the laser in a darkened corner with a box on the top so students won't stare at the light.
Instruct students to put each of the slits in front of the light and record what they see. The light will get elongated which illustrates that the light is actually diffracted or "flaring outward. This is called interference. Do not expect students to know what actually causes this. Answer: electromagnetic light ; diffraction Instruct students to hit the tines of a tuning fork in kit and place the tines on the surface of the water.
Waves will move from the center of vibration. Notice that the pattern spreads from the center and causes little ripples. This shows not only diffraction but also interference similar to that in station 2. Answer: physical wave; diffraction Using a spoon, instruct students to hit the surface of the water in a pan of water. The ripples should be large enough to hit the end of the pie tin and reflect backwards.
However, students might only see the spreading outward and call this diffraction. One student should push back several of the coils and then release them.
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