POLARIZATION ELECTROMAGNETIC An electromagnetic wave propagates in

POLARIZATION

ELECTROMAGNETIC An electromagnetic wave propagates in a direction that is at right angles to the vibrations of both the electric and magnetic oscillating field vectors. The two fields are mutually perpendicular. WAVE The wavelength and frequency of electromagnetic waves are related by: c = λ·ν

FEATURES OF ALL ELECTROMAGNETIC WAVES The wave travels in vacuum with a definite and unchanging speed: c =1/√ε 0μ 0 = 3· 108 m/s The instantaneous magnitudes of E and B in an electromagnetic wave are related by the expression: E =c·B Unlike mechanical waves, which need the oscillating particles of a medium such as water or air to transmit a wave, electromagnetic waves require no medium.

PLANE ELECTROMAGNETIC WAVE The electric and magnetic fields of a sinusoidal plane electromagnetic wave propagating in the positive x direction can be written E=Emax cos(kx - ωt) B=Bmax cos(kx - ωt) ω - the angular frequency of the wave k =2π/λ - the angular wave number.

The electromagnetic spectrum includes waves covering a broad range of wavelengths, from long radio waves at more than 104 m to gamma rays at less than 10 -14.

Electromagnetic waves may differ in frequency and wavelength but the relationship in vacuum holds for each: c = λ·ν ν – the frequency of the light (Hz), λ –the wavelength of the light (m).

VISIBLE LIGHT We can detect only a very small segment of this spectrum directly through our sense of sight – visible light. Its wavelengths range from about 380 to 750 nm, with corresponding frequencies from about 790 to 400 THz. Different parts of the visible spectrum evoke in humans the sensations of different colors. Ordinary white light includes all visible wavelengths. The sensitivity of the human eye is a function of wavelength, being a maximum at a wavelength of about 5. 5· 10 -7 m. With this in mind, why do you suppose tennis balls often have a yellow-green color?

UNPOLARIZED LIGHT An ordinary beam of light consists of a large number of waves emitted by the atoms of the light source. Each atom produces a wave having some particular orientation of the electric field vector , corresponding to the direction of atomic vibration. Any actual light source contains a tremendous number of atoms with random orientations, so the emitted light is a random mixture of waves linearly polarized in all possible transverse directions. Such light is called unpolarized light or natural light. The arrows show a few possible directions of the waves in the beam

THE DIRECTION OF POLARIZATION A wave is linearly polarized if the resultant electric field vibrates in the same direction at all times at a particular point. Sometimes, such a wave is described as plane-polarized, or simply polarized. The plane formed by E and the direction of propagation is called the plane of polarization of the wave. In this example, the direction of polarization is along the y-axis. The direction of polarization of an electromagnetic wave always is the direction of the electric-field vector not the magnetic field, because many common electromagnetic-wave detectors respond to the electric forces on electrons in materials, not the magnetic forces.

METHODS OF POLARIZATION It is possible to transform unpolarized light into polarized light. Polarized light waves are light waves in which the vibrations occur in a single plane. The process of transforming unpolarized light into polarized light is known as polarization. There a variety of methods of polarizing light: selective absorption reflection double refraction scattering

POLARIZING FILTERS The most common technique for polarizing light. Uses a material incorporates substances that have dichroism. Dichroism a selective absorption in which material transmits waves whose electric field vectors lie in the plane parallel to the polarizing axis and absorbs waves whose electric field vectors are perpendicular to that direction. Developed originally by the American scientist Edwin H. Land. He called the material polaroid

POLAROID In 1938, E. H. Land (1909– 1991) discovered a material, which he called polaroid, that polarizes light through selective absorption by oriented molecules. This material is fabricated in thin sheets of long-chain hydrocarbons. The sheets are stretched during manufacture so that the long-chain molecules align. After a sheet is dipped into a solution containing iodine, the molecules become good electrical conductors. Conduction takes place primarily along the hydrocarbon chains because electrons can move easily only along the chains. As a result, the molecules readily absorb light whose electric field vector is parallel to their length and allow light through whose electric field vector is perpendicular to their length.

POLAROID It is common to refer to the direction perpendicular to the molecular chains as the transmission axis. In an ideal polarizer: All light with E parallel to the transmission axis is transmitted; All light with E perpendicular to the transmission axis is absorbed.

MALUS'S LAW When unpolarized light is incident on an ideal polarizer the intensity of the transmitted light is exactly half that of the incident unpolarized light, no matter how the polarizing axis is oriented: I 0 = ½ Inat I 0 – intensity of the polarized light is transmitted through the polarizer, Inat – intensity of unpolarized light is incident on an polarizer.

MALUS'S LAW The intensity of the polarized beam transmitted through the second polarizing sheet (the analyzer) varies as: I = I 0 cos 2θ I 0 is the intensity of the polarized wave incident on the analyzer. This is known as Malus's law and applies to any two polarizing materials whose transmission axes are at an angle of θ to each other.

MALUS'S LAW The intensity of the transmitted beam is a maximum when the transmission axes are parallel: θ = 0 or 180 o The intensity is zero when the transmission axes are perpendicular to each other. This would cause complete absorption.

INTENSITY OF POLARIZED LIGHT, EXAMPLES The intensity of light transmitted through two polarizers depends on the relative orientation of their transmission axes. (a) The transmitted light has maximum intensity when the transmission axes are aligned with each other. (b) The transmitted light has lesser intensity when the transmission axes are at an angle of 45° with each other. (c) The transmitted light intensity is a minimum when the transmission axes are perpendicular to each other.

POLARIZATION BY REFLECTION When an unpolarized light beam is reflected from a surface, the reflected light may be: Completely polarized Partially polarized Unpolarized It depends on the angle of incidence If the angle is 0°, the reflected beam is unpolarized For other angles, there is some degree of polarization For one particular angle, the beam is completely polarized

POLARIZATION BY REFLECTION, PARTIALLY POLARIZED EXAMPLE When unpolarized light is incident on a reflecting surface, the reflected and refracted beams are partially polarized.

BREWSTER’S LAW Unpolarized light is incident on a reflecting surface The reflected beam is completely polarized The refracted beam is perpendicular to the reflected beam The angle of incidence θp is Brewster’s angle The refracted beam is partly polarized Brewster’s law relates the polarizing angle to the index of refraction for the material

Polarization by reflection is a common phenomenon. Sunlight reflected from water, glass, and snow is partially polarized. If the surface is horizontal, the electric field vector of the reflected light has a strong horizontal component. Sunglasses made of polarizing material reduce the glare of reflected light. The transmission axes of the lenses are oriented vertically so that they absorb the strong horizontal component of the reflected light. If you rotate sunglasses through 90 degrees, they are not as effective at blocking the glare from shiny horizontal surfaces.

POLARIZATION BY DOUBLE REFRACTION Solids can be classified on the basis of internal structure. Those in which the atoms are arranged in a specific order are called crystalline. Those solids in which the atoms are distributed randomly are called amorphous. When light travels through an amorphous material, such as glass, it travels with a speed that is the same in all directions. That is, glass has a single index of refraction. In certain crystalline materials, however, such as calcite and quartz, the speed of light is not the same in all directions. Such materials are characterized by two indices of refraction. Hence, they are often referred to as double-refracting or birefringent materials.

POLARIZATION BY DOUBLE REFRACTION, RAYS Unpolarized light splits into two plane-polarized rays: the ordinary (O) ray and the extraordinary (E) ray. The two rays are in Mutual perpendicular directions ( Indicated by the dots and arrows 0

POLARIZATION BY DOUBLE REFRACTION, RAYS The ordinary (O) ray is characterized by an index of refraction of no. This is the same in all directions The second ray is the extraordinary (E) ray which travels at different speeds in different directions. Characterized by an index of refraction of n. E that varies with the direction of propagation

POLARIZATION BY DOUBLE REFRACTION, OPTIC AXIS There is one direction, called the optic axis, along which the ordinary and extraordinary rays have the same speed: n. O = n. E The difference in speeds for the two rays is a maximum in the direction perpendicular to the optic axis. A point source S inside a double-refracting crystal produces a spherical wave front corresponding to the ordinary ray and an elliptical wave front corresponding to the extraordinary ray. The two waves propagate with the same velocity along the optic axis.

POLARIZATION BY SCATTERING When light is incident on any material, the electrons in the material can absorb and reradiate part of the light. Such absorption and reradiation of light by electrons in the gas molecules that make up air is what causes sunlight reaching an observer on the Earth to be partially polarized. You can observe this effect—called scattering—by looking directly up at the sky through a pair of sunglasses whose lenses are made of polarizing material. Less light passes through at certain orientations of the lenses than at others.

POLARIZATION BY SCATTERING An unpolarized beam of sunlight traveling in the horizontal direction strikes a molecule, setting the electrons of the molecule into vibration. These vibrating charges act like the vibrating charges in an antenna. The horizontal component of the electric field vector in the incident wave results in a horizontal component of the vibration of the charges, and the vertical component of the vector results in a vertical component of vibration.

POLARIZATION BY SCATTERING If the observer is looking straight up (perpendicular to the original direction of propagation of the light), the vertical oscillations of the charges send no radiation toward the observer. Thus, the observer sees light that is completely polarized in the horizontal direction, as indicated by the brown arrows. If the observer looks in other directions, the light is partially polarized in the horizontal direction

POLARIZATION BY SCATTERING Some phenomena involving the scattering of light in the atmosphere can be understood as follows. When light of various wavelengths λ is incident on gas molecules of diameter d, where d<<λ, the relative intensity of the scattered light varies as 1/λ 4. The condition d<<λ is satisfied for scattering from oxygen (O 2) and nitrogen (N 2) molecules in the atmosphere, whose diameters are about 0. 2 nm. Hence, short wavelengths (blue light) are scattered more efficiently than long wavelengths (red light). Therefore, when sunlight is scattered by gas molecules in the air, the short-wavelength radiation (blue) is scattered more intensely than the long-wavelength radiation (red).