# POLARIZATION OF LIGHT WAVES

## Presentation on theme: "POLARIZATION OF LIGHT WAVES"— Presentation transcript:

POLARIZATION OF LIGHT WAVES
we described the transverse nature of electromagnetic waves. Figure shows that the electric and magnetic field vectors associated with an electromagnetic wave are at right angles to each other and also to the direction of wave propagation.

An ordinary beam of light consists of a large number of electromagnetic waves emitted by the atoms or molecules of the light source. The vibrating charges associated with the atoms act as tiny antennas. Each atom produces a wave with its own orientation of, as in Figure , corresponding to the direction of atomic vibration.

all directions of vibration are possible, the resultant electromagnetic wave is a superposition of waves produced by the individual atomic sources. The result is an unpolarized light wave, represented schematically in Figure 24.25a. Note that all directions of the electric field vector are equally probable and lie in a plane (such as the plane of this page) perpendicular to the direction of propagation.

linearly polarized A wave is said to be linearly polarized if the resultant electric field vibrates in the same direction at all times at a particular point, as in Figure 24.25b. such a wave is described as plane polarized or simply polarized The wave in Figure is an example of a wave that is linearly polarized in the y-direction. As the wave propagates in the x-direction, is always in the y-direction.

However, because all directions of vibration are possible, the resultant electromagnetic wave is a superposition of waves produced by the individual atomic sources. The plane formed E-vector by and the direction of propagation is called the plane of polarization of the wave. It’s possible to obtain a linearly polarized beam from an unpolarized beam by removing all waves from the beam except those with electric field vectors that oscillate in a single plane. We now discuss three processes for doing this: (1) selective absorption, (2) reflection, and (3) scattering.

Polarization by Selective Absorption
The most common technique for polarizing light is to use a material that transmits waves having electric field vectors that vibrate in a plane parallel to a certain direction and absorbs those waves with electric field vectors vibrating in directions perpendicular to that direction. In 1932, E. H. Land 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, which are stretched during manufacture so that the molecules align. After a sheet is dipped into a solution containing iodine, the molecules become good electrical conductors. However, conduction takes place primarily along the hydrocarbon chains, because the valence electrons of the molecules can move easily only along those chains. (Recall that valence electrons are “free” electrons that can move easily through the conductor.)

As a result, the molecules readily absorb light having an electric field vector parallel to their lengths and transmit light with an electric field vector perpendicular to their lengths. It’s common to refer to the direction perpendicular to the molecular chains as the transmission axis.

Polarizing material reduces the intensity of light passing through it
Polarizing material reduces the intensity of light passing through it. In Active Figure 24.26, an unpolarized light beam is incident on the first polarizing sheet, called the polarizer; the transmission axis is as indicated. The light that passes through this sheet is polarized vertically, and the transmitted electric field vector is . A second polarizing sheet, called the analyzer, intercepts this beam with its transmission axis at an angle of θ to the axis of the polarizer.

The component of that is perpendicular to the axis of the analyzer is completely absorbed. The component of that is parallel to the analyzer axis, E0 cos θ, is allowed to pass through the analyzer. Because the intensity of the transmitted beam varies as the square of its amplitude E, we conclude that the intensity of the (polarized) beam transmitted through the analyzer varies as Malus’s law where I0 is the intensity of the polarized wave incident on the analyzer

This expression, known as Malus’s law, applies to any two polarizing materials having transmission axes at an angle of θ to each other. Note from Equation that the transmitted intensity is a maximum when the transmission axes are parallel (θ = 0 or 180°) and is zero (complete absorption by the analyzer) when the transmission axes are perpendicular to each other.

EXAMPLE Unpolarized light is incident upon three polarizers. The first polarizer has a vertical transmission axis, the second has a transmission axis rotated 30.0° with respect to the first, and the third has a transmission axis rotated 75.0° relative to the first. If the initial light intensity of the beam is Ib, calculate the light intensity after the beam passes through (a) the second polarizer and (b) the third polarizer. Solution: Calculate the intensity of the beam after it passes through the second polarizer: The incident intensity is Ib/2. Apply Malus’s law to the second polarizer: Calculate the intensity of the beam after it passes through the third polarizer. The incident intensity is now 3I b/8. Apply Malus’s law to the third polarizer: 75.0° ° =45.0°

Polarization by Reflection
When an unpolarized light beam is reflected from a surface, the reflected light is completely polarized, partially polarized, or unpolarized, depending on the angle of incidence. If the angle of incidence is either 0° or 90° (a normal or grazing angle), the reflected beam is unpolarized. For angles of incidence between 0° and 90°, however, the reflected light is polarized to some extent. For one particular angle of incidence the reflected beam is completely polarized. Suppose an unpolarized light beam is incident on a surface, as in Figure

The beam can be described by two electric field components, one parallel to the surface (represented by dots) and the other perpendicular to the first component and to the direction of propagation (represented by brown arrows). It is found that the parallel component reflects more strongly than the other components, and this result in a partially polarized beam. In addition, the refracted beam is also partially polarized.

Now suppose that the angle of incidence, θ1, is varied until the angle between the reflected and refracted beams is 90° (Fig b). At this particular angle of incidence, called the polarizing angle θp, the reflected beam is completely polarized, with its electric field vector parallel to the surface, while the refracted beam is partially polarized. we see that at the polarizing angle, θp +90° +θ2 = 180°, so that θ2 = 90° - θp.

Using Snell’s law and taking n1 = nair = 1.00 and n2 = n yields
Because sin θ2 = sin(90° -θp) = cos θp, the expression for n can be written Equation is called Brewster’s law, and the polarizing angle θp is sometimes called Brewster’s angle after its discoverer, Sir David Brewster

Example: The critical angle for total internal reflection for sapphire surrounded by air is 34.4°. Calculate the polarizing angle for sapphire. Solution:

Example: Unpolarized light passes through two polaroid sheets. The axis of the first is vertical, and that of the second is at 30.0° to the vertical. What fraction of the incident light is transmitted? Solution:

Example: Plane-polarized light is incident on a single polarizing disk with the direction of E0 parallel to the direction of the transmission axis. Through what angle should the disk be rotated so that the intensity in the transmitted beam is reduced by a factor of (a) 3.00, (b) 5.00, (c) 10.0? Solution:

Example: Three polarizing disks whose planes are parallel are centred on a common axis. The direction of the transmission axis in each case is shown in Figure P38.42 relative to the common vertical direction. A plane-polarized beam of light with E0 parallel to the vertical reference direction is incident from the left on the first disk with intensity Ii = 10.0 units (arbitrary). Calculate the transmitted intensity If when (a) θ1 = 20.0°, θ 2 =40.0°, and θ 3 = 60.0°; θ 1 =0°, θ 2 = 30.0°, and θ 3= 60.0°. Solution:

Polarization by Scattering
When light is incident on a system of particles, such as a gas, the electrons in the medium can absorb and reradiate part of the light. The absorption and reradiation of light by the medium, called scattering, is what causes sunlight reaching an observer on Earth from straight overhead to be polarized.

When the beam strikes the air molecule, it sets the electrons of the molecule into vibration. These vibrating charges act like those in an antenna except that they vibrate in a complicated pattern. The horizontal part of the electric field vector in the incident wave causes the charges to vibrate horizontally, and the vertical part of the vector simultaneously causes them to vibrate vertically. A horizontally polarized wave is emitted by the electrons as a result of their horizontal motion, and a vertically polarized wave is emitted parallel to the Earth as a result of their vertical motion. Scientists have found that bees and homing pigeons use the polarization of sunlight as a navigational aid.

Example: How far above the horizon is the Moon when its image reflected in calm water is completely polarized? (nwater =1.33) Solution

Liquid Crystals An effect similar to rotation of the plane of polarization is used to create the familiar displays on pocket calculators, wristwatches, notebook computers, and so forth. The properties of a unique substance called a liquid crystal make these displays (called LCD’s, for liquid crystal displays) possible. As its name implies, a liquid crystal is a substance with properties intermediate between those of a crystalline solid and those of a liquid; that is, the molecules of the substance are more orderly than those in a liquid, but less orderly than those in a pure crystalline solid.

The forces that hold the molecules together in such a state are just barely strong enough to enable the substance to maintain a definite shape, so it is reasonable to call it a solid. However, small inputs of mechanical or electrical energy can disrupt these weak bonds and make the substance flow, rotate, or twist. The liquid crystal is placed between between two glass plates that have electrodes attached similar to those depicted in the illustration below. The glass plates are drawn with seven black electrodes that can be individually charged (these electrodes are transparent to light in real devices).

When a voltage is applied across any segment in the display, that segment turns dark. In this fashion, any number between 0 and 9 can be formed by the pattern, depending on the voltages applied to the seven segments.

Light passing through polarizer 1 is polarized in the vertical direction and, when no current is applied to the electrodes, the liquid crystalline phase induces a 90 degree "twist" of the light and it can pass through polarizer 2, which is polarized horizontally and is perpendicular to polarizer 1. This light can then form one of the seven segments on the display. When current is applied to the electrodes, the liquid crystalline phase aligns with the current and loses the cholesteric spiral pattern. Light passing through a charged electrode is not twisted and is blocked by polarizer 2. By coordinating the voltage on the seven positive and negative electrodes, the display is capable of rendering the numbers 0 through 9. In this example the upper right and lower left electrodes are charged and block light passing through them, allowing formation of the number "2".

Polarization is also used in the entertainment industry to produce and show 3-D movies. Three-dimensional movies are actually two movies being shown at the same time through two projectors. The two movies are filmed from two slightly different camera locations. Each individual movie is then projected from different sides of the audience onto a metal screen. The movies are projected through a polarizing filter. The polarizing filter used for the projector on the left may have its polarization axis aligned horizontally while the polarizing filter used for the projector on the right would have its polarization axis aligned vertically.

Consequently, there are two slightly different movies being projected onto a screen. Each movie is cast by light that is polarized with an orientation perpendicular to the other movie. The audience then wears glasses that have two Polaroid filters. Each filter has a different polarization axis - one is horizontal and the other is vertical. The result of this arrangement of projectors and filters is that the left eye sees the movie that is projected from the right projector while the right eye sees the movie that is projected from the left projector. This gives the viewer a perception of depth.

The liquid crystal is placed between two glass substrates that are packaged between two pieces of Polaroid material with their transmission axes perpendicular. A reflecting surface is placed behind one of the pieces of Polaroid.

A reflecting surface is placed behind one of the pieces of Polaroid
A reflecting surface is placed behind one of the pieces of Polaroid. First consider what happens when light falls on this package and no voltages are applied to the liquid crystal, as shown in Figure. Incoming light is polarized by the polarizer on the left and then falls on the liquid crystal. As the light passes through the crystal, its plane of polarization is rotated by 90o, allowing it to pass through the polarizer on the right.

It reflects from the reflecting surface and retraces its path through the crystal.
Thus, an observer to the left of the crystal sees the segment as being bright. When a voltage is applied as in Figure , the molecules of the liquid crystal don’t rotate the plane of polarization of the light. In this case, the light is absorbed by the polarizer on the right and none is reflected back to the observer to the left of the crystal. As a result, the observer sees this segment as black. Changing the applied voltage to the crystal in a precise pattern at precise times can make the pattern tick off the seconds on a watch, display a letter on a computer display, and so forth.