A Fundamental Property of Anisotropic Media
Until now we have confined our attention to the propagation of light in isotropic media, i.e., substances whose optical properties are the same in all directions. Liquids, as well as amorphous solid substances such as glass and plastics, are usually isotropic because of the random distribution of the molecules. In many crystals, the optical as well as the other physical properties are different in different directions. This optical anisotropy, often referred to as double refraction, or birefringence, is due to the particular arrangement of the atoms in the crystalline lattice and, is found to produce many curious and interesting phenomena, which we propose now to investigate.
We start with a simple experiment. A parallel beam of monochromatic light passes through a polariscope formed, for example, by two sheet polarizers, and then falls upon a screen. We rotate the analyzer until the light spot on the screen disappears. The transmission axis of the analyzer is then perpendicular to that of the polarizer i.e., the polarizer and the analyzer are crossed). Between the analyzer and the polarizer we now insert a thin, plane-parallel plate cut from a birefringent crystal obtained by cleavage. The light on the screen will, in general, reappear. The analyzer being rotated, the light intensity will change periodically between a maximum and a minimum, but will not become zero for any position of the analyzer. We thus conclude that the light emerging from the plate is no longer linearly polarized.
After removing the plate, we again place the analyzer and the polarizer in the crossed position, reinsert the birefringent plate, and rotate it in its own plane. For each complete turn, we find four positions, at 90° to one another, for which the light spot on the screen disappears. We conclude that the light now emerging from the plate has the same linear polarization as the light incident upon the plate. We can check this conclusion by rotating the analyzer and noting that the corresponding variation of the transmitted light intensity follows the law of Malus. It is thus possible to trace on the plate two mutually perpendicular lines such that a linearly polarized light wave vibrating in a direction parallel to either line traverses the plate without changing its state of polarization. We сall these lines the axes of the plate.
By generalizing this result, we can describe the fundamental property of optically anisotropic medium as follows: for every direction of propagation there are only two waves vibrating in one or the other of two mutually perpendicular planes that preserve their state of polarization while traveling through the medium.
|
|
|
Consider now a wave which, upon entering the plate, is linearly polarized, but does not vibrate in either of the two preferred directions. We may regard the incident wave as the superposition of two linearly polarized waves vibrating in the two preferred directions. If the velocities of propagation of these two waves were the same, the two component waves after traversing the plate would recombine into a linearly polarized wave with the same plane of vibration as the incident wave. Since we know from experiment that this is not the case, i.e. since we know the state of polarization of the wave to change on traversing the plate, we conclude that the velocities of propagation in an anisotropic medium of the waves vibrating in the two preferred directions are different. We can, of course, check this conclusion directly by measuring (e.g. with an interferometer) the velocities of propagation through a birefringent plate of the two waves whose planes of vibration contain one or the other of the two axes of the plate.
(unknown source)
Rainbows
Rainbows are the most famous of many extraordinary displays that can be seen in the sky. Everybody seems to love them, from children to old men, and few wouldn't stop at least a few seconds to admire a fully developed rainbow. It has to do, undoubtedly, with its beautiful sequence of colors; but also with its perfect geometrical shape against the random background of clouds. If one could see the polarization of the rainbow, a new order would become apparent: the rainbow is strongly polarized. Indeed, with a polarizer its contrast significantly improves and you can find otherwise undetectable rainbows!
Rainbows form the arc of a perfect circle centered on the shadow of your head. Yes, that's right. Everybody sees a slightly different rainbow even if standing side by side: each one has his own personal rainbow! If you are not sure where a rainbow should appear during rainy weather do the following. Look for the shadow of your head on the ground; that's the center of the circle (antisolar point). Next, find the radius by stretching in a line your two hands (thumb to thumb) at arm length. Of course, if the tip of your finger doesn't reach above the horizon, then the sun is too high for a rainbow.
|
|
|
The drops of water refract and reflect the rays from the sun backwards, at 42 degrees to the incoming rays. Thus, the rainbow is seen in a direction opposite to the sun as a circle of that radius, an angular size of which is independent of your distance to the raindrops. This is also true for the rainbow produced by a watering hose: no matter how much you step back, you won't be able to include its full diameter in your photograph (you need a very-wide-angle lens for that). Of course, when you step back, the individual drops forming the arch will change. The largest rainbow (half a circle) appears when the sun is close to the horizon. However, from airplanes, mountains or tall towers, where one can see raindrops below the horizon, the rainbow can be as large as a full circle.
Two refractions (A,B) and one internal reflection (C) inside the spherical water drops form the primary rainbow. A secondary rainbow, which sometimes appears outside the primary one (at 51 degrees) is caused by two internal reflections instead of just one. An interesting side note: small raindrops remain almost perfectly spherical falling through the air; very large raindrops are deformed but, contrary to popular belief, they are flattened vertically instead of becoming elongated and pear-shaped as the archetypal cartoonish drop.
The color sequence of the rainbow is caused by the two refractions (A,B) as red is refracted slightly less than blue. On the other hand, the polarization of the rainbow is caused by the internal reflection (C). The rays strike the back surface of the drop close to the Brewster angle, so almost all the light reflected is polarized perpendicular to the incidence plane (perpendicular to the monitor screen). This is similar to the way the glare of the sun on the sea is polarized, except that now the reflecting surface is not horizontal. As the incidence plane is determined for each drop by the plane containing the sun, the drop, and the observer, the rainbow is polarized tangential to the arch. Thus, a vertical polarizing filter will produce a gap at the top of the rainbow while enhancing the contrast of the sides.
|
|
|
The primary rainbow is 96% polarized while the secondary is 90% polarized. The extra brightness of the sky inside the primary rainbow (and outside the secondary rainbow) is also polarized tangentially (but to a lesser degree) as it has the same origin as the bows. With a filter pointing radially it disappears together with the rainbows and becomes undistinguishable from the dark Alexander's band between the bows (named after Alexander of Aphrodisius, AD 200).
(http://polarization.com/index-net/index.html)
[1] would be produced by... – обычно создается...
[2] continue unperturbed – остаются без изменений
[3] a master – эталон
[4] b. – the written abbreviation of born;
[5] ca. – a written abbreviation of circa (=about).
[6] it will no longer suffice – теперь будет недостаточно
[7] at most - самое большее
[8] at two angular positions of the second sheet 180 apart - в двух угловых положениях через 180°
[9] at angular positions halfway between - в угловых положениях на половинном угле поворота, т.е. 90°
Дата добавления: 2019-09-13; просмотров: 187; Мы поможем в написании вашей работы! |
Мы поможем в написании ваших работ!