Polarization of Light
The restrictions of the vibrations of light in a particular directions is called polarization of light.
When an unpolarized light, consisting of the vibrations of electric field vector distributed symmetrically in all the directions and perpendicular to the direction of its propagation, passes through a tourmaline crystal, all the vibrations are restricted except those which are parallel to its crystallographic axis AD as shown in Fig. 8.01. given above. Therefore, on emerging through the crystal, the vibrations no longer remain symmetrical about the direction of propagation of the wave but are confined to a single plane called plane of vibration. (Polarization of Light)
Plane of vibration: The plane that contains the vibrations of a plane polarized light after emerging out of the polarizer, is called plane of vibration. ABCD is the plane of vibrations as shown in Fig. 9.01. (Polarization of Light)
Plane of polarization: The plane in which the vibrations are restricted due to polarization is called plane of polarization and it is always perpendicular to the plane of vibration. PQRS is the plane of polarization shown in Fig. 9.01.
Plane Polarized light: As per electromagnetic theory of light, the electric vector associated with an electromagnetic waves, exhibits all optical phenomena and so is also called light vector. In a plane polarized light, the vibrations are restricted to a particular fixed plane so that the vibrations are normal to the direction of propagation of light. (Polarization of Light)
Detection of plane polarized light
The polarizer alone or the nacked eyes can not distinguish between the unpolarized and a plane polarized light. in order to analyze the plane polarized light, we use second tourmaline crystal called analyzer.
An unpolarized light is allowed to pass through a tourmaline crystal or a Nicol prism, the emerging light is plane polarized, so this crystal is called as Polarizer. When the polarizer is rotated about the path of ordinary light, it is observed that the intensity of the light transmitted from the polarizer remains unchanged because of the reason that the plane polarized light is obtained in each of the orientation of the polarizer, which has the vibrations in a direction parallel to the axis of the crystal in that orientation. (Polarization of Light)
As shown in [Fig. 8.02], the intensity of light is observed to be unaffected and maximum, when the analyzer is rotated in the path of the light transmitted from the polarizer, such that the axes of the both, polarizer and analyzer become parallel to each other. On the other hand, when the axes of the both, polarizer and analyzer become perpendicular to each other, the intensity of light out of the analyzer is reduced to minimum or more appropriately the light is extinguished, as shown in [Fig. 8.03]. At this moment, the polarizer and the analyzer are said to be in crossed position.
Polarization by reflection
A plane polarized light can be produced by reflection of light, which is a very simple method.
It was observed by Malus, that an ordinary light beam, when reflected from a transparent medium becomes partially polarized and the degree of polarization is a function of the angle of incidence of the light beam. As the angle of incidence increases, the degree of polarization also increases and the reflected ray becomes completely polarized at a particular angle of incidence, called as polarizing angle for that medium. The value of polarising angle also depends upon the wavelength of light. Therefore, the complete polarization can be obtained only with monochromatic light. (Polarization of Light)
As shown in [Fig. 8.04], an ordinary light wave is incident on an interface XX* separating the two media, air and a denser medium of refractive index (mu) along AO. When the incidence is made at polarizing angle, then the reflected component as OR is found to be completely plane polarized and the refracted component OK will be unpolarized light. The plane polarized light has the vibrations normal to the plane of paper. (Polarization of Light)
Therefore, the conclusion is drawn that the vibrations perpendiculars to the plane of papers or parallel to the reflecting surface are reflected along OR, when the light is incident at the polarising angle, while the other vibrations are transmitted which make some angle with the reflecting surface. (Polarization of Light)
Brewster’s Law
This law states that the refractive index of a medium is equal to the tangent of the polarising angle when the light is incident at the interface of the refracting medium at an angle of incidence equal to the polarising angle.
Suppose that the polarising angle and the refractive index of the refracting medium be p and mu respectively, then according to the Brewster’s Law, we can write,
The reflected light beam will be perfectly plane polarized as the light is incident at polarising angle p. Let r be the angle of refraction, then according to Snell’s law in refraction of light, we can write,
Since, r + p =90o, therefore, it can be proved that the reflected ray is normal to the refracted ray. Thus, when when a light ray is made to incident at polarising angle, then the reflected ray is found to be totally plane polarised and is at right angle to the refracted ray. (Polarization of Light)
Polarization by scattering
The scattering is a phenomenon associated with the interaction of energy with the matter such that the energy is absorbed by the matter in one direction and its re-radiation takes place in all possible directions. (Polarization of Light)
When a beam of light waves is passed through a medium made of the particles of size comparable to the wavelength of the light waves, then these light waves are scattered from the particles constituting the medium, in all possible directions. It is observed that the scattered light in the direction perpendicular to the direction of the incident beam is a plane polarised light. This sort of technique provides us the method to produce the plain polarized light by the method of scattering. (Polarization of Light)
Let us consider that a beam of unpolarized light is propagating along X-axis and its vibrations are confined in YZ-plane as shown in [Fig. 8.05]. This light beam interacts with the matter particle at a point O and the scattering takes place. After the scattering at point O, the light scattered along the Y-axis possess only those vibrations which are normal to it and parallel to the Z-axis. On the other side, the light scattered along the Z-axis possess only those vibrations which are normal to it and parallel to the Y-axis. Thus, the light scattered along both the axes, Y-axis and Z-axis are plane polarised light. (Polarization of Light)
Law of malus
This law states that the intensity of an emergent light is directly proportional to the square of the cosine of the angle between the planes of the transmission of the analyser and the polariser when a completely plane polarised light is made to incident on an analyser. (Polarization of Light)
Let us suppose that the plane of polariser and the plane of analyser are inclined at an angle theta with each other and the plane polarised light of intensity I0 and an amplitude of a is made to incident on the polariser. Now resolving the amplitude of the incident light wave in to the two components, (Polarization of Light)
(1) The cosine component along the direction of the plane of transmission of the analyser and is represented as
(2) The sine component in a direction perpendicular to the plane of transmission of the analyser and is represented as
The Intensity of light transmitted out of the analyser, on the assumption that there is no loss of light energy due to absorption while traversing the analyser, is given by
This gives the mathematical expression of the Malus Law.
Discussion:
(1) when the analyser and polariser are parallel to each other implying that theta = 0o or 180o so that cos (theta)= +1 or -1, Therefore, I = Io. ( maximum Intensity). Hence , the intensity of light transmitted out of the analyser is maximum and equal to that which falls on the analyser from the polariser, if the polariser and the analyser are parallel to each other. (Polarization of Light)
(2) When (theta) = 90o, so that cos(theta)= 0, Therefore, I = 0. Hence, the intensity of light transmitted out of the analyser is zero (minimum), if the polariser and the analyser are perpendicular to each other. (Polarization of Light)
(3) The variation of the intensity of light with the change in the angle between the polariser and analyser can be studied with the help of the graph as shown below, (Polarization of Light)
(4) When the unpolarised light is made to incident on the analyser, then the intensity of the light transmitted out of the analyser will be I = I0/2. It is due to the reason that the light vector, in case of unpolarised light, vibrates randomly in a plane perpendicular to the direction of propagation, therefore, the intensity of transmitted light is determined by putting the average value of cos2 (theta) in above eqn. which is cos2 (theta) = 1/2. (Polarization of Light)
Nicol prism
A beam of unpolarized light, when is made to incident over a calcite crystal (Iceland spar), two beams of polarised light are produced on account of its internal molecular structure. These two polarised light components are called as Ordinary Rays (O-Rays) and Extraordinary Rays (E-Rays). The vibrations of these two polarised light components are perpendicular to each other. On rotating the crystal about the line of vision, it is observed that the E-Ray also rotates but about the O-Ray and due this unusual and different behaviour, these are called extraordinary rays. (Polarization of Light)
Construction:
Nicol prism is generally used for producing and detecting the polarised light. It is made for of calcite crystal having refractive index 1.66 for ordinary rays and 1.49 for extraordinary rays. The face of calcite crystal, having the angles of 72o and 108o is cut into two halves along the diagonal AB. Canada balsam having refractive index equal to 1.55 for both types of rays (O-rays and E-rays) is used for cementing the two halves together as shown in [Fig. 8.08]. (Polarization of Light)
Working of Nicol prism
Two polarised beams of ordinary (O-Ray) and extraordinary (E-Ray) are produced when an unpolarised beam of light is allowed to be incident on the crystal at large angles. The light beam of polarised extraordinary light emerges out of the crystal and the polarised beam of ordinary light travelling through the calcite crystal ((denser medium) falls on the cementing layer of Canada balsam acting as the rarer medium, at an angle greater than the critical angle for calcite- Canada balsam interface and hence it will readily undergo total internal reflection as shown in [Fig. 8.08]. Both of the light beams consisting of ordinary (O-Rays) and extraordinary (E-Rays) are plane polarised. (Polarization of Light)
Polaroids
As very large crystals of calcite and tourmaline are not practically available, therefore, a tourmaline crystal or A Nicol prism can not be used to produce plane polarised beam of light of large cross-section. (Polarization of Light)
The polaroids are the thin and large sheets of crystalline polarising material, made artificially, which produce plane polarised beams of large cross-section efficiently.
The synthetic small needle shaped crystals of iodosulphate of quinine, as discovered by Herapath in the year of 1852, possesses the property of polarising the light called as herapathite. These crystals can not be used as such because they are not stable and can not bear even a smaller strain, therefore, a polaroid sheet is prepared from the suspension of these crystals in nitrocellulose and its thin sheet is mounted between the two sheets glass or celluloid in order to provide the stability. (Polarization of Light)
Alternatively, a polaroid sheet can be obtained from the sheet of polyvinyl alcohol. The molecules of such a sheet get oriented, when such a sheet is subjected to a large strain and this orientation of the molecules of the sheet takes place in the direction of the applied strain. When the sheet is impregnated with iodine, then its material becomes dichroic. The dichroic crystals are those doubly refracting crystals like tourmaline, having an additional property that it absorbs ordinary and extraordinary rays unequally. This phenomenon is called as selective absorption or dichroism. The polaroid sheet so obtained is called H-polaroid. (Polarization of Light)
The stretched sheet of polyvinyl alcohol becomes more strongly dichroic as well as very strong, when it is heated in presence of a dehydrating agent like HCl. Such type of a polaroid sheet is called as K-polaroid. (Polarization of Light)
The mechanical strength and support to each polaroid sheet is provided by enclosing each one between the thin glass plates. Further, a polaroid has a characteristic plane called transmission plane. When unpolarised light falls on a polaroid, only the vibrations parallel to the transmission plane get transmitted.
applications of polaroids
The polaroids have a variety of applications their uses and a few of them are mentioned here.
(1) In sun glasses: The polaroids used as sun glasses in goggles are more efficient and usable as compared to the goggles made of coloured glasses. Polaroids sun glasses protect our eyes from the glare.
(2) In wind shields of automobiles: The polaroids are fairly used in manufacturing the wind shields of an automobile. Such types of wind shields made of polaroids protect effectively the eyes of the drivers of the vehicles in night from the dazzling light of the vehicles approaching in front sides. The covers of head lights of the vehicles made of the polaroids due to the same reason.
(3) In window panes: The window panes of trains and particularly of aeroplanes are made of the polaroids in order to have a better control over the light entering into the trains or aeroplanes through their windows.
(4) In three dimensional motion pictures: The pictures taken from the stereoscopic camera, create three dimensional effects when viewed through the polaroids spectacles.
Key points:
*The phenomenon of polarization establishes that the light is transverse in nature.
*The vibrations in the plane polarised light are perpendicular to the plane of polarization.
*A polariser alone can not distinguish between an unpolarised light and a plane polarized light.
*The light reflected from a transparent refractive medium is always a plane polarised, however the degree of polarization depends upon the angle of incidence.
* When a light ray is made to incident on a transparent refracting surface, at an angle equal to the polarising angle, then the refracted and the reflected ray are perpendicular to each other.
*When the angles between the principal sections of two Nicol prisms are 0o and 180o, they are termed as the parallel Nicols and when the angle is 90o, then they are said to be the crossed Nicols.
*C. V. Raman and his collaborators in Calcutta investigated the scattering of light by molecules in nineteen twenties and was awarded Nobel Prize in Physics for this work in 1930.
