Summary:
+ + Reflection Introduction
+ + Diffraction Refraction
+ Telescope and spherical aberration
+ Dispersion and Telesopio Newton
luminiferous ether
+ + birefringence Polarization and Interference
+
- Rainbow
Reflection and Refraction
Read Fresnel
A drop of water
Many drops of water
Two rainbows
Reflection and Refraction
During the preceding chapters we have seen how, in the seventeenth century were the phenomena including Reflection and Refraction . Such understanding, however, was limited to the "laws of the corners, and the relation between the angles of incidence and reflection / refraction when a ray of light crosses the boundary between two different materials (eg air / , water or air / glass).
The two phenomena coexist almost always the case classic is a piece of glass through which light passes (refraction), but from which is also reflected. Not only that these phenomena occur multiple times at both surfaces of the glass:
A ray of light coming from the top left, reaches the glass plate in step 1. A certain amount of light is reflected (red beam), the remainder enters the glass due to the second angle of refraction (blue ray). When this beam of light reaches the opposite side of the glass, in paragraph 2, is the complementary phenomenon: a portion of light is refracted outside (red beam), while the remaining is reflected back into the glass. The mechanism is repeated in steps 3, 4, 5 ... in theory, indefinitely. ▲
Read Fresnel
If you want to calculate the exact total of how much light passes through the glass, and how much is reflected, is not sufficient know the laws of the corners as Snell's Law, but it would take even more quantitative is precisely the Laws of Fresnel.
The Fresnel laws which take into account the angle of the light, the coefficients of refraction materials involved, and also Polarization of light: in fact we use the plural, "the" laws of Fresnel, which are two floors to be used as the polarization of the incident light. And since no complications never end, we must also take into account the variation of the coefficients of refraction depending on the color of light: it is the phenomenon of dispersion , discovered by Newton.
Now that you have made the list of the phenomena involved in the production of the rainbow, we can begin to explain its functioning. Although the programs I have written to create the images that follow take into account as accurately as possible of all aspects of the matter, the explanation is very basic, those interested in mathematical details of the laws involved ... can find a lot of material on the web, on the other hand I have often consulted too! ▲
A drop of water
To get a rainbow requires sunlight and a few drops of water. Let's see what happens then a single ray of light hitting a single drop of water (it is not very different to what has been described on the glass plate). Note: For now we will see phenomena "profile", ie having the sun on our left instead of behind us: the only way you can see the path drawn by the rays of incoming light from the sun, and their subsequent reflections / refractions.
1 - The light coming from the left (green ray in the figure above left) hits the drop in point 1. A certain amount of light is reflected depending on the angle β (red line), while the remaining light is refracted into the drop depending on the angle γ (blue line).
2 - The light refracted in step 1 continues its course and once again meets the surface of the drop in point 2 (top right): here is the complementary phenomenon to that described in paragraph 1, in fact, a portion is refracted outside the drop (red line) while the remaining still remains and is reflected inside the drop (blue line).
3, 4 - In the lower left and right we see a repetition of the phenomenon described in Section 2. In reality the mechanism is repeated many times: that is, until the drop in the light beam continues to be reflected, with diminishing intensity ... in theory an infinite number of times!
For now, the study of the rainbow we will analyze These four beams of light exiting from the drop: as already mentioned there are others, but they contribute only marginally to the phenomenon we are studying (we will discuss at the end).
The animation that follows, for every ray of light that comes on the drop (white lines, left) out four red rays, the result of the various phenomena of reflection / refraction described above:
It sounds very chaotic: this is because you are not yet taking into account the intensity of these rays, but only of their angles. We see happening now also taking into account this aspect
image above you see the intensity of light produced separately by each of the four types of light that comes out of the drop of water in the upper left of the first reflection in the top right and then down the three phenomena of reflection / refraction faced by the rays of light as they "bounce" on the inner surface of the drop.
The intensity of these four beams of light are very different from one another. The beam is brighter than the second, in fact, the percentage of light that comes out of it immediately in the drop is far greater than the amount of light that follows the other routes (such how, in a window, the light passing through it is in quantities well above the light that is reflected).
How can we now see the overlap of all phenomena, without being "dazzled" by the most intense? Just ignore it right! In fact, let's see what happens from this beam of light if you move away from the drop:
As a focus point near the drop you have a very high peak brightness, move the light is dispersed very quickly, and Seen from far away that there will be between the observer and the drops that give rise to the rainbow, the effect caused from this beam of light becomes negligible.
In the following you see the composition of the beams of light in their real intensity between them, by not only the beam above:
To the right one can see, very weak, twin beams of light resulting the reflection of light when it encounters the drop for the first time: this phenomenon can be neglected. What is rather interesting to have sharp lines, the result of the third and fourth refraction: it is these lines will give rise to two rainbows, the primary and secondary.
far we have seen what happens using only red light: Let's see what happens now superimposing the effect generated by beams of light of all colors:
brighter at the ends of the lines on the left, one can see the colored fringes: these are due to different refraction coefficient associated with each color of light, so its lines of greater intensity are released with slightly different angles from each other.
a little get away 'from the drop:
The two beams intersect, and the fringes are always more colorful. Get away again:
Now we took the drop off the screen, there are no more high-brightness peaks around the droplet itself, which forced them to take the low image brightness, and now with optimum brightness, you can clearly see the two beams of light, color as if they were passed through a prism, even if the rainbow is a combination of factors much more complicated. ▲
Many drops of water
In short, we have seen "what comes" from a drop of sunlit water. But what an observer sees exactly that look from afar?
depends. In the sense that depends on the mutual position between drops and eye. If the observer is in position 1, its eye is red-lit arc primary, if in position 2 or 3, green or purple the same period.
If the observer is in position 4 or 5, sees the red bow secondary one due to the fourth reflection / refraction of the light beam inside the drop. The secondary rainbow has the following features:
- the colors arranged in reverse order (this is due to the fact that light rays undergo compared to the rainbow reflection in the primary);
- is wider (reflection additional amplification due to differences in the corners);
- has less color (each reflection / refraction follows a decrease of ' intensity of the light beam).
image above I have indicated the position 6: This shows a dark band called "Band of Alexander". In fact, while outside of the area between the two beams of light has a diffuse glow, the inner zone is not reached by any ray of light coming out of the drop (except for that which results from the first reflection of sunlight, but that weak start, with the distance is lost very quickly to become negligible). The Alexander which gives its name to the dark band is Alexander of Aphrodisias, greek philosopher of the third century AD, who was the first to describe this phenomenon.
In the above we understood what would an observer moving within the beams of light emitted from a single drop. Of course, what really happens is the reverse phenomenon: the observer is stationary and is hit by the beams of light reaching it from a myriad of different drops.
image above left point of view, indicated by the eye, is hit by the red primary bow, then the viewer has the impression that the drop "and" just in red. On the right hand is the eye's light green bow secondary here is that this other drop is green.
The rainbow is created by a myriad of drops placed in different positions from each other. Here's what the observer sees (the image that follows the rainbow is seen "profile"):
It is evident that all the drops "colored" in red are perfectly within primary aligned with the observer, as well as the drops are aligned with all other colors: this is because the sun's rays are all parallel to each other, and the geometric aspects of the reflections / refractions are the same for each drop. Then, the condition that they show all the drops of a certain color (red in this case), the only prerequisite is that the angle α between the arrival direction of sunlight (the white lines, from left) and the line connecting the drop to the observer, must be constant for the red primary bow, the angle is about 42 degrees. ▲
Two rainbows
As I said, the images above show how a side view of the rainbow, because there is still nothing resembling a bow! The chart below shows instead the phenomenon in perspective:
For every drop you have to take into account the plane lying on the line from the sunlight that illuminates it, and passes from the eye of the observer (the 'area shaded in gray indicates the plan for the drop 1). If the angle α between the line of incident light (shown in white) and the line che congiunge la goccia con l'osservatore è proprio di 42,5° allora l'osservatore vedrà quella goccia illuminata di rosso; altrimenti l'osservatore vedrà il colore associato a un angolo diverso... oppure nessun colore.
Vediamo la cosa da un altro punto di vista: l'area di cielo che si colorerà di rosso sarà il "luogo" delle gocce che stanno al vertice di un angolo di 42,5°, misurato fra la linea di luce che illumina la goccia e la congiungente fra goccia e osservatore. Questo luogo non può che essere circolare: è come se usassimo un compasso con apertura costante (ecco quindi spiegata la forma di arco circolare dell'arcobaleno).
Il discorso ovviamente vale for any other color / angle: smaller angles result in concentric arcs of smaller radius. The angles larger for the secondary rainbow, giving rise to the arcs of greater radius for just that second rainbow angles intermediate cause darker band between the two: the Gang of Alexander.
Finally, finally we see a rainbow seen from the front. In the following image (the same that's in the opening) I superimposed a picture taken from the web of a double rainbow to the image obtained by the computer. The program calculates the sum of the contributions of light reaching the observer for each color (which corresponds to a different indice di rifrazione, e una diversa composizione RGB, rosso-verde-blu) per ogni goccia, tenendo conto anche della polarizzazione della luce a ogni evento. Direi che la somiglianza è davvero notevole... ▲
Ulteriore arcobaleno
Per finire, manca un accenno alla questione lasciata in sospeso: cosa succede delle ulteriori riflessioni / rifrazioni all'interno di ciascuna goccia?
Ecco qui i raggi generati dalle due successive rifrazioni: have the same characteristics as those described above and are also able to generate a rainbow. However, they have much weaker intensity of the first two, and only done in extreme weather you can appreciate the most intense of the two. Which, unlike the first two, but should not be tried with his back to the sun: this is to be ephemeral rainbow against the sun, here is also explained why it is so difficult to observe. ▲
0 comments:
Post a Comment