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  Speed of light        The Obstacles to the light      Polarization of the light
  Lighting and light intensity   Strength, Work, Power and Energy     Footer

Physics - Speed of Light :

"1st PART"     PHYSICS

In the first chapter of this physics lesson, we will deepen the knowledge we have about light : how it propagates, how fast, what is its constitution ... ?

The second, will allow us to specify the meaning that we must attribute to the terms : strength - work - power - energy.


What light is is a problem which has occupied the minds of most scholars of all time and which has also interested all people curious about natural phenomena. More particularly from the year 1 600, and for almost three hundred years, physicists wondered if the light consisted of very small corpuscles, in other words, if it had a corpuscular aspect, or indeed waves which propagated in space like the waves on the water and the sound in the air, that is to say if it had an undulatory aspect.

This seems like an easy problem to solve. Indeed, each of us could distinguish without too much difficulty the movement of a corpuscle going from one place to another, from a wave movement which is propagated by widening around its own source. In reality, there are reasons to be puzzled. It is that after having carried out various experiments, some made acceptable the corpuscular idea, others made it possible rather to retain the undulatory aspect.

By considering these two aspects, we can compare a beam of light crossing space with a band of seals moving on the surface of the sea (Figure 1-a).


Each seal simultaneously represents a corpuscle of light and a light wave. Indeed, although moving with his companions from one point to another on the surface of the sea, and this while keeping a well defined direction, he follows, where he is, the ripple of the waves.

The three rectilinear lines which compose the strip, while always keeping in good order, bring us back to the idea of the light ray which, in the Figure 1-b, is represented by a straight line of yellow color.

This comparison is only figurative and cannot give any explanation regarding the true nature of light. If we want to know a little more, we have to examine the behavior of light rays in the most significant cases.

We will describe in this lesson the main light phenomena, limiting ourselves to their observation.

Light rays can be seen in summer, when, after a thunderstorm, the sun appears between the clouds. They can also appear when a beam of light enters a small hole through a dark room. These images give an idea of the trajectory of the light ray and highlight the following fundamental property : Light propagates in a straight line, at least as long as it does not encounter an obstacle.


In the empty (or almost empty) spaces that separate the stars, there are torrents of light that cross and go in all directions, all at the same fantastic speed.

For a long time, it was thought that light moved away from its source at an infinite speed, which means that we assumed that it propagated instantly from one point to another in space, whatever the length of the course. But this is a mistake : the light always takes a certain time to go from one point to another.

The speed of light being assumed to be very high, it proved necessary to measure this time, to consider a very long course. It is very naturally the astronomers best placed to have such routes : earth-moon ; terre-soleil ; ... And it was indeed one of them who had the first opportunity to measure this speed. Towards the end of the 17th century, the Dutch astronomer ROEMER, who was observing the movements of Jupiter and four of its satellites, noted that the latter, under certain conditions, had notable delays with respect to their chart in space.

This fact requires an explanation, because all the stars, large and small, are always very punctual.

ROEMER, after numerous observations, succeeds in determining with great accuracy the revolution of a satellite of the planet Jupiter. In addition, he knows that the earth and Jupiter revolve around the sun. Using these data and performing numerous and complex calculations, it determines the points where Jupiter and its satellite must be located on a given day, at a specific hour and minute.

ROEMER then undertakes to verify by astronomical observation the accuracy of its calculations. To this end, it waits that the Earth and Jupiter are in conjunction, that is to say both aligned with the sun, The earth being in the middle as shown in the Figure 2-a. He then notes the exact moment when the Jupiter satellite enters the Shadow zone of the planet.


It then calculates in how long the three planets will be aligned, but this time with the sun in the middle (Figure 2-b). The Earth and Jupiter are then in opposition. In addition, his calculations allow him to specify the moment when the Jupiter satellite will disappear in the Shadow cone.

His observations lead him to note, with surprise, that the penetration of the satellite behind its planet takes place later than the calculations predicted. This delay is 1 000 seconds. ROEMER is looking for the cause, being certain of the accuracy of its calculations and observations. He then notices that the Earth, when it is in opposition with Jupiter, is more distant from this planet than when it is in conjunction. He then calculates that the difference in distances between opposition and conjunction is about 298 million km.

ROEMER then explains the delay observed as follows : if the path of the light sent by the satellite to the Earth has been lengthened by 298 million kilometers and the delay observed is 1 000 seconds, this means that this time is that necessary for light to travel 298 million kilometers.

Starting from these two numbers, it is easy to calculate the speed of light. Indeed, by dividing a distance traveled by the time taken to travel it, we obtain the speed. In our case, we find 298 000 km / s. ROEMER can therefore say that light propagates in outer space at the fantastic speed of 298,000 km / s.

Subsequently, after ROEMER's experience, other measurements were carried out under different conditions and with sophisticated measuring instruments. It has thus been established that the speed of propagation of light in a vacuum is 299 776 km / s, a speed slightly higher than that which ROEMER had found. In practice, this number is rounded to 300 000 km / s, as mentioned in Figure 2.


Light is born from matter, that is, from the substances that make up bodies. A simple light bulb puts this claim into action.

The sole purpose of the electric current flowing through the tungsten wire of the bulb is to heat it until its temperature is 3 000° C. At this time, the wire emits light in the form of rays and in all directions.

It would be interesting to see how heat can be transformed into light. To do this, we would need to know more about the structure of matter, which will be done later. For the moment, we will limit ourselves to following the path of the light rays, noting the causes which deviate them from their natural rectilinear direction or which modify their color.

Anyone can observe what happens when a beam of colored light is projected onto a white body.

If the light is red, the white body appears red to us ; if it is yellow the body appears yellow to us, if it is green, the body appears to us green and so on.

White can only be seen in natural light, which is white, or in the almost white light of a bulb.

These observations lead us to think that the color of the bodies is due, in part, to the type of light they receive. Contrary to what happens with the white body, we can observe that a black body, but a matt black, always appears black in any light.

The perception of black indicates the absence of light. In a completely dark room, you can see that the white, black or colored bodies are all black and cannot be distinguished. On the other hand, if we observe a black body successively under different types of light, we see that it never takes the color of the light which illuminates it.

The white body, which colors differently depending on the type of lighting, shows that substances can return the rays that strike them. On the other hand, the black body erasing all traces of light, shows that the substances can absorb the rays which strike them.

The first phenomenon, in which the rays are returned in all directions (Figure 3), is called the phenomenon of light scattering

The second phenomenon, in which the rays are absorbed, is called the phenomenon of absorption of light.


Note that these two phenomena occur simultaneously and more or less each time a material obstacle is in the path of a ray.

The absorption and diffusion of light are the main causes of body coloring. They also make it easy to demonstrate that white light is actually a mixture of colored lights.

Take for example two objects, one red, the other green. Why this difference in color since both lit by the same white light ?

The observer sees the red object, because this object diffuses rays of red light ; similarly the observer sees another green object because the latter diffuses rays of green light. One can think that the matter constituting the two bodies transforms white light into red light and into green light. This is not the case !

The reason is that white light is made up of red, orange, yellow, blue, indigo and purple lights, with all the graduations. Thus, the red object presents this color under white light because it absorbs all the colored lights constituting white light except the red light which it diffuses around it. Similarly, the green object appears green to us because it absorbs all the colors of white light except the green that it diffuses around it.

However, there are materials which do not constitute an insuperable obstacle to the path of light rays.

Let us consider for example the Figure 4-a. The ray arriving on the surface of the glass, called the incident ray, changes direction as soon as it enters the thickness of glass where it is neither diffused nor absorbed.


After having followed a straight course throughout the thickness of the glass, it leaves it by resuming its initial direction but offset with respect thereto.

The change in direction of the light ray from air to glass and then from glass to air is called refraction.

The phenomenon of refraction occurs each time a light ray passes from a transparent medium into another which is also transparent.

For example, it occurs when the light passes from the air into the water, or vice versa, as one sees Figure 4-b while following the course of the rays which go from the seagull to the eye of the fish.

Note in this figure that due to refraction, the fish sees the seagull in a place where it is not and therefore it may not perceive the danger that threatens it.

We said about the Figure 4-a that the ray leaving the glass resumed its initial direction but shifted compared to this one. It should be noted that this only occurs when the two sides of the transparent body, the side through which the ray enters the body and the side through which it exits, are parallel. Otherwise, it is quite different.

Let us consider for example the prism represented Figure 4-c. If the incident ray is a pure colored light, that is to say of a single color which is said to be still monochrome, at the exit of the prism the ray has a variable inclination according to its color. Thus, violet light has the greatest deviation. The other colored lights undergo weaker deviations. We observe that the refraction is less and less pronounced as the colors change from purple to red.

If, instead of a monochrome light, white light is used as the incident ray, we observe that at the exit of the prism we obtain a range of colored lights revealing in white light all the colors going from purple to red.

These phenomena of decomposition and dispersion of white light are the basis of the rainbow and the multicolored sparkle of the crystals. In the case of the rainbow, the function of the prism is fulfilled by the innumerable droplets of water which, after a storm, are carried by the winds.


Up to now we have considered three types of obstacle which can appear on the way of a light ray.

  • The white (or colored) body which diffuses all (or part) of the incident light ;

  • The black (or colored) body which absorbs all (or part) of the incident light ;

  • The transparent body, which leads to the formation of phenomena of refraction, decomposition and dispersion.

Three particular cases still remain to be examined. The first is that of the reflecting surface : the mirror (Figure 5).


Unlike the white body, the mirror is not limited to reflecting the incident rays in all directions. The rays it returns, called reflected rays, are directed in well-defined directions all obeying the same law called the law of reflection. This law reads as follows :

The incident ray and the reflected ray form with the perpendicular to the point of incidence two equal angles between them called angle of incidence and angle of reflection (Figure 5).

In this figure, the angle of incidence is designated by the symbol (^i) and the angle of reflection by the symbol (^r). The circumflex accents on the letters ^i and ^r remind us that we designate angles. The angle of incidence and the angle of reflection being equal, one can abbreviate to write ^i = ^r.

The same figure shows that the eye receiving the rays coming from the cone and reflected by the mirror is deceived as was the eye of the fish in the phenomenon of refraction. Indeed, the eye seems to extend the rays reflected behind the mirror and reconstruct the image of the cone there. But this is, of course, an illusory image also called virtual image, and turned towards the real object. Likewise, when we look at ourselves in a mirror, our face constitutes the real object and our image that we see is the virtual image.

We can observe that the real object and its virtual image are symmetrical.

This symmetry can be checked very simply.

  • Taking as a reference the base of the mirror, we see that :

  • - the object and the image are at the same height ;

  • - the object on the one hand and the image on the other hand are at the same distance from the surface of the mirror ;

  • - the object and the image look at each other.

Let us now examine another phenomenon, that illustrated in Figure 6. Note in passing that his study shows us that the idea of the light ray is accepted with some reservations.

In this new experiment, we drop a cone of monochrome light, a red light for example, on a glass plate striped vertically by fine, parallel and very tight incisions (Figure 6).


The glass, at the points where it is engraved, becomes almost opaque and therefore does not allow light to pass through. On the other hand, between each pair of grooves there is a thin strip of glass through which the light rays can pass freely.

Under the conditions of the experiment, we can therefore expect to see appear on the screen as many fine bands of light and shadow as there are transparent strips and opaque grooves. However, it does not happen that way.

On the screen indeed appear lighted and dark bands but much wider and also much more marked than you would expect. On the other hand, the number of illuminated strips is lower than that of the transparent strips.

It can therefore be deduced therefrom that the light rays coming from the grid do not arrive on the screen and that consequently they would be likely not to propagate in a straight line.

This singular behavior of light passing through a very thin slit is called the diffraction phenomenon.

Diffraction therefore shows that light does not always propagate like a ray. However, it is hard to imagine that some rays are destroyed. In reality, everything happens as if some of them are strengthening and others are weakening. The result is that observed on the screen : very bright bands and others very black.

The phenomenon is similar to that of sound : two sound waves propagated giving rise to the phenomenon of interference. This resulted in a strengthening or weakening of the resulting wave which gave rise to an intense or weak or even non-existent sound. In the present case, two or more rays add up giving rise to a more intense light or, on the contrary, they contradict each other by determining a large black band. This goes against the law of the rectilinear propagation of light rays.

The similarity with sound waves leads us to say that with light there can be interference of waves. Light is therefore made up of light waves, it is its wave aspect.

The Figure 7 shows another experiment, the results of which can lead to even greater perplexity.


In this experiment, we observe that two crystals of a transparent material, tourmaline, arranged in a given position, let light pass. If one of the crystals is rotated, the light no longer passes. This phenomenon is explained if one resorts to the wave aspect of light.

The light wave can propagate in all directions. However, in our experience, we assume that tourmaline only transmits a light wave oriented in a well-defined manner with respect to the crystal. More precisely, the ray leaving the first crystal can pass through the second only if the latter is in the same position as the first.

By turning one of the crystals, the light vibrates between them in such a way that it cannot pass through the second. We can therefore consider that it is stopped by the latter which then behaves like an opaque body. The effect produced by crystals of this type is called polarization of light.

The polarization of light is the basis for the operation of certain filters for cameras. In this application, we eliminate the reflections forming on the shiny surfaces of certain objects and particularly undesirable in the case of color photography.


The most common light effect that everyone notices daily is the lighting of premises : home, workplace, shops ... This light effect is commonly called lighting.

Each of us could see that the lighting of a body depended on the distance between it and the light source. It suffices to approach and move a flashlight away from any object to see that when the lamp is near the object, it appears well lit, when on the contrary the lamp is moved away, the object becomes less well-lit.

The influence of the light source-object distance having been established, let us make sure to measure it.

Let us consider the small installation represented Figure 8-a and composed of a lamp and two screens of different surfaces.


Let's light up the small screen placed 2.5 m from the lamp. Let us measure with a special device (photocell) the lighting of the screen. Suppose the number indicated by the cell is 20.

Now let's light up the large screen placed this time 5 m from the lamp, Figure 8 shows that the same amount of light falls on both screens. But, by measuring with the same cell the lighting of the large screen, that is to say its brightness or the amount of light rays it returns, the number indicated by the device is no longer 20 but 5, that is to say four times less.

We have just found that by doubling the source-screen distance, we divided the brightness by 4. We can therefore state an important law :

The lighting is inversely proportional to the square of the distance.

(Math lessons explain what is meant by "inversely proportional" and "square").

If therefore, in our experience the lamp-large screen distance had been 7.5 m, that is to say 3 times that of the lamp-small screen, the lighting would have been 3 x 3 = 9 times less ; if instead of 3 times it had been 4 times, the lighting would become 4 x 4 = 16 times less ....

The Figure 8-b represents an experiment which is used to compare the quantity of light emitted by two light sources S1 and S2.

The screen, which is represented there, is opaque over the entire surface, except the central circle (C) which is translucent, that is to say semi-transparent such as for example an oil stain on a sheet of paper.

If the light intensity of the source S1 is greater than that of the source S2, a certain amount of light coming from S1 filters through the circle (C) towards S2 and vice versa. However, if the two light intensities are equal, the illumination of the area (C) is equal on both sides of the screen and therefore, no light filters either on one side or the other. This results in the disappearance of the stain.


2. 1. - STRENGTH

2. 1. 1. - DEFINITION

We call force all that is capable :

  • to deform a body ;

  • to put a body in motion if it is at rest or to stop it if it is in motion ;

  • to modify the movement of a body.

Examples :

On a workbench, let's block a steel bar by one of its ends. Press in B in the direction of arrow F. We note that the bar is deformed and takes position B' (Figure 9-a).

Attach to a hook C, a coil spring R. Let us pull the free end in the direction of the arrow F. We note that the spring lengthens (Figure 9-b).


In these two experiences, there is a deformation of a body. As long as the effort does not exceed a certain value, the bar and the spring resume their original form when this effort ceases : it is said to have elastic deformation.

Now consider a piece of wood B placed on a table T (Figure 9-c). It remains motionless if nothing moves it. On the other hand, it cannot set itself in motion. But if we pull it along the arrow F, it moves : it's the setting in motion. If you stop pulling it, it stops almost immediately : it stops movement due to friction forces. Finally, if we drop a paper ball at point A, it falls in B, just below A. But if a draft occurs, it falls in C : there has been a modification of the movement by force the wind ...

A man, an animal, water, wind, water vapor, a magnet ... are capable of exerting forces.

2. 1. 2. - EQUAL FORCES

Definition : We say that two forces are equal when they produce, under the same conditions, the same elastic deformation of a body.

Thus, in the experiment represented Figure 9-a, if a person pressing on the bar makes lower the end until B' then that another raises it in the same place, until B", the distances B - B' and B - B" being equivalent, it is said that the two people exerted equal forces. We can then write F = F'.

We will also say that these people exert equal forces if, simultaneously, one pressing and the other lifting at the same point on the bar, the latter does not undergo any deformation. We then say that the two forces are balanced.


If we support, without letting it rest on a support, a mass of one kilogram, we say that we exert on this mass a vertical force directed from the bottom up by a kilogram-weight (kgp). This force is balanced by the weight of this mass of 1 kilogram which is also a force of one kilogram-weight, but directed vertically from top to bottom.

The kilogram-weight (kgp), although still used, is an old unit of measurement. The official unit is the Newton whose symbol is N. The relationship between these units is given by the following equality : 1 kgp = 9.81 N. The sub-multiple of Newton is the dyne which is 0.000 01 N or 10- 5 N.


A force can be broken down into a number of components. Thus, in the experiment of the Figure 9-b :

  • point B where the force is exerted is its point of application ;

  • the xy axis in which the spring is pulled is called the line of action or direction of the force ;

  • the direction in which the spring moves under the action of force is quite naturally its direction ;

  • the elongation of the spring is a function of the magnitude of the force, also called intensity, which is expressed in Newton or in dyne.

A force is therefore characterized by four elements : its point of application, its direction, its direction and its intensity.

When a force applied to a body moves this body, in other words, when a force moves its point of application, it is said that there is production of work.

2. 2. - JOB

If we raise to 1 meter from the ground a body whose weight is 1 kgp (which amounts to moving by one meter, in its own direction, the point of application of a force of one kgp) we say that the work of force is one kilogrammeter (kgm). Similarly, if we pull a cart with a force of 1 kgp and make it travel a meter, we will also say that the work of force is one kilogrammeter. More generally, when the displacement takes place in the direction of the force, the work W of the force expressed in kilogrammeters, is equal to the product of the force (kgp) by the length of the displacement (in meters). Hence the formula :

W = F . l

This relation clearly shows that there is work only if there is displacement ; but the displacement must be carried out in the direction of the force.

The kilogrammeter is also an old unit. The legal unit is Joule (J) and its value compared to the previous one is given by the relation : 1 kgm = 9.81 J. The sub-multiple is the erg which is worth 0.000 0001 J = 10-7 J.

In the previous relation, the units to be used are therefore Joule (J) for work W, Newton (N) for force F, meter (m) for the length of the displacement. We then write :

W(J) = F(N) . l(m)

2. 3. - POWER

The work done by an electric motor gives insufficient information about its capabilities. So an engine that does a certain job in a minute is not the same one that does the same job in a second. To be more precise, we will then say that the second engine is sixty times more powerful than the first because it can do the same job in sixty times less time. We define the power P of an engine as the work it can do in a second, and more generally : the power is the work provided in a second. From this definition, we obtain the relation :

P = W / t

The unit of power is the watt (W) and its multiple is the kilowatt (kW) which obviously is worth 1 000 watts. The old unit, still found on the nameplates of the engines, is the horsepower (ch) which is worth 736 W.

The previous relationship expressed with the units becomes :

P(W) = W(J) / t(s)

Note that if the work done is 1 joule in 1 second, we can then say that the watt is the joule per second (J / s)

The watt, which is the mechanical power unit, is also the electric power unit. Finally, note the relationship between the two old units of power (cheval) and work (kgm) : 1cv = 75 kgm / s.

2. 4. - ENERGY

2. 4. 1. - DEFINITION

A body is said to have energy when it is able to do work.

2. 4. 2. - UNIT AND SYMBOL

Energy is expressed as work in joule and has the same symbol W.


Let be a body (C) stopped in B, 5 m from the ground and weighing 600 Newtons (which is equivalent to approximately 60 kgp) Figure 10-a.

Let it drop without giving it speed at the start (we also say : without initial speed). This body takes under the action of its weight, which is a constant force in size and direction, a uniformly accelerated movement which brings it to the ground at point D.


Between points B and D, the work done by the force F of 600 newtons is :

WJ = FN . lm

WJ = 600 . 5 = 3 000 J

During the movement, this work is stored in the body which arrives at D with a certain speed. This gives it what is called kinetic energy. This can for example be translated into D by the driving in of a stake. We then say that the kinetic energy of the body C in D is 3 000 joules.

Pile driving machines, called "sheep", and pounder hammers are based on this principle.

This kinetic energy of 3 000 joules would drive a stake 3 cm that would resist sinking with a constant force of 100 000 newtons :

W(J) = F(N) . l(m)

3 000 J = 100 000 x 0,03

We will remember that the kinetic energy of a body is the energy acquired during its movement.

Note now that when the body C is stopped at B, the force which acts on it and due to its weight, does not work since there is no displacement. However, this body is capable of producing work, so it has energy. We will say that this energy is in the potential state or that it is potential energy.

We will remember that the potential energy of a body is the energy that this body has when it is at rest.


Let us consider the Figure 10-b with the body successively in B, N, D.

1 - In B, its kinetic energy is zero, since it is not in motion.

Its potential energy is :

W(J) = F(N) . l(m)

W(J) = 600 x 5 = 3 000 joules

We then have : Potential energy + kinetic energy = 0 + 3 000 = 3 000 joules

2 - The body is in N :

Its kinetic energy is :

W(J) = F(N) . l(m)

W(J) = 600 x 3 = 1 800 joules

Its potential energy is :

W(J) = 600 x 2 = 1 200 joules

We have at this point :

Potential energy + kinetic energy : 1 800 + 1 200 = 3 000 joules.

3 - The body is in D.

Its kinetic energy is, as we have already calculated, 3 000 J.

Its potential energy is zero (the body can no longer fall).

So now we have :

   Potential energy + kinetic energy = 0 + 3 000 = 3 000 joules.

We see that at all times the sum of the kinetic energy and the potential energy is constant. When kinetic energy appears, an equal amount of potential energy disappears.

This principle is general. This is the principle of energy conservation.


Energy comes in many forms :

  • water from a dam (potential energy) falling (kinetic energy) on the turbine blades produces mechanical energy ; in turn, the turbines drive alternators and the mechanical energy is transformed into electrical energy ;

  • An electric oven transforms electrical energy into heat energy ;

  • the chemical energy of a battery or accumulator is transformed into electrical energy ;

  • the starter fitted to the engine of a car transforms the electrical energy it receives from the accumulator into mechanical energy ...

There are still many other forms of energy : nuclear energy, solar energy, wind energy (wind energy) ...

Finally, we will note that the energy is reversible. That is to say, for example, that mechanical energy can be transformed into electrical energy and vice versa ; electrical energy can be transformed into mechanical energy.


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