Course : Bachelor of Applied Physical Science

IInd Year (Semester IV)

Paper no : 14

Subject : PHPT – 404 Electricity, Magnetism and

Electromagnetic Theory

Topic No. & Title : Topic – 1 Electrostatics

Lecture No : 20

Tittle : Polarization

IntroductionHello friends during our discussion on electromagnetic waves in the previous lecture we concluded that an electromagnetic wave consists of oscillating electric and magnetic fields, then we established that the various possible frequencies of electromagnetic waves form a spectrum, a small part of which is visible light and finally we learnt that an electromagnetic wave traveling along an x axis has an electric field and a magnetic field with magnitudes that depend on x and t. Today we shall try to identify that an electromagnetic wave transports momentum and can exert a force and a pressure on a target and then we shall discuss polarization of the electromagnetic wave.

Radiation Pressure

After going through this section of the lecture we shall be able to

Distinguish between force and pressure

Identify that an electromagnetic wave transports momentum and can exert a force and a pressure on a target.

For a uniform electromagnetic beam that is perpendicular to a target area, apply the relationships between that area, the wave’s intensity, and the force on the target, for both total absorption and total backward reflection

Electromagnetic waves transport linear momentum and thus can exert a pressure on an object when shining on it has been measured with an apparatus called torsion balance as shown here.

A mirror (a perfect reflector) and a black disk (a perfect absorber) are connected by a horizontal rod suspended from a fine fiber. Normal-incidence light striking the black disk is completely absorbed, so all of the momentum of the light is transferred to the disk. Normal-incidence light striking the mirror is totally reflected, and hence the momentum transferred to the mirror is twice as great as that transferred to the disk. The radiation pressure is determined by measuring the angle through which the horizontal connecting rod rotates. The apparatus must be placed in a high vacuum to eliminate the effects of air currents.

The pressure exerted, however, must be very small because, for example, you do not feel a punch during a camera flash but you can always find an expression for the pressure, let us shine a beam of electromagnetic radiation for a time interval t. We shall assume in this discussion that the electromagnetic wave strikes the surface at normal incidence and transports a total energy U to the surface in a time t. We further, assume that the object is free to move and that the radiation is entirely absorbed by the object. Maxwell showed that, if the surface absorbs all the incident energy U in this time, the total momentum p transported to the surface has a magnitude

p=Uc

…… A

The pressure exerted on the surface is defined as force per unit area F/A. Let us combine this with Newton’s second law:

P= FA

= 1A

dpdt

If we now replace p, the momentum transported to the surface by light, from Equation A, we have

P= 1A

dpdt

= 1A

ddt (U

c )=1c

(dU /dt )A

We can write

dUdt

=∆ U

We recognize ΔU as the rate at which energy is arriving at the surface per unit area, which is the magnitude of the Poynting vector. Thus, the radiation pressure P exerted on the perfectly absorbing surface is

P= Sc

……B

Here do note that Equation B is an expression for uppercase P i.e. the pressure, while Equation A is an expression for lowercase p i.e. linear momentum.

If the surface is a perfect reflector (such as a mirror) and incidence is normal, then the momentum transported to the surface in a time t is twice that given by Equation A. That is, the momentum transferred to the surface by the incoming light is

p=Uc

and that transferred by the reflected light also is

p=Uc

.

Therefore,

p=2 Uc

The momentum delivered to a surface having a reflectivity somewhere between these two extremes has a value between

Uc

∧2U

c,

depending on the properties of the surface. Finally, the radiation pressure exerted on a perfectly reflecting surface for normal incidence of the wave is

P=2 Sc

Polarization

The orientation of VHF (very high frequency) television antennas is not the same everywhere. It could be horizontal or vertically. The difference is due to the direction of oscillation of the electromagnetic waves carrying the TV signal. In India, the transmitting equipment is designed to produce waves that are polarized vertically; that is, their electric field oscillates vertically. Thus, for the electric field of the incident television waves to drive a current along an antenna and provide a signal to a television set, the antenna must be vertical. In North America, the waves are polarized horizontally. The objectives of learning in this section would be to:

Distinguish between polarized light and unpolarized light.

For a light beam headed toward you, sketch representations of polarized light and unpolarized light.

When a beam is sent into a polarizing sheet, explain the function of the sheet in terms of its polarizing direction (or axis) and the electric field component that is absorbed and the component that is transmitted.

Distinguish between a polarizer and an analyzer.

This Figure here shows an electromagnetic wave with its electric field oscillating parallel to the vertical y axis. The plane containing the electric field vectors is called the plane of oscillation of the wave (hence, the wave is said to be plane-polarized in the y direction). We can represent the wave’s polarization i.e. state of

being polarized, by showing the directions of the electric field oscillations in a head-on view of the plane of oscillation, as in Fig. b. The vertical double arrow in that figure indicates that as the wave travels past us, its electric field oscillates vertically — it continuously changes between being directed up and down the y axis.

Polarized Light

The electromagnetic waves emitted by a television station all have the same polarization, but the electromagnetic waves emitted by any common source of light such as the Sun or a bulb are polarized randomly or unpolarized. That is, the electric field at any given point is always perpendicular to the direction of travel of the waves but changes directions randomly. Thus, if we try to represent a head-on view of the oscillations over some time period, we do not have a simple drawing with a single double arrow like that of Fig. b; instead we have a mess of double arrows like the one shown in this Figure.

….A

In principle, we can simplify the mess by resolving each electric field into y and z components. Then as the wave travels past us, the net y component oscillates parallel to the y axis and the net z component oscillates parallel to the z axis. We can then represent the unpolarized light with a pair of double arrows as shown.

….B

The double arrow along the y axis represents the oscillations of the net y component of the electric field. The double arrow along the z axis represents the oscillations of the net z component of the electric field. In doing all this, we effectively change unpolarized light into the superposition of two polarized waves whose planes of oscillation are perpendicular to each other — one plane contains the y axis and the other contains the z axis. One reason to make this change is that drawing Fig. B is a lot easier than drawing Fig. A.

We can draw similar figures to represent light that is partially polarized (its field oscillations are not completely random as in Fig. A, nor are they parallel to a single axis as in Fig. B). For this situation, we draw one of the double arrows in a perpendicular pair of double arrows longer than the other one.

Polarizing Direction

We can transform unpolarized visible light into polarized light by sending it through a polarizing sheet, as is shown here.

Such sheets, commercially known as Polaroids or Polaroid filters, were invented in 1932 by Edwin Land while he was an undergraduate student. A polarizing sheet consists of certain long molecules embedded in plastic. When the sheet is manufactured, it is stretched to align the molecules in parallel rows, like rows in a plowed field. When light is then sent through the sheet, electric field components along one direction pass through the sheet, while components perpendicular to that direction are absorbed by the molecules and disappear.

We shall not stay on the molecules but, instead, shall assign to the sheet a polarizing direction, along which electric field components are passed.

Thus, the electric field of the light emerging from the sheet consists of only the components that are parallel to the polarizing direction of the sheet; hence the light is polarized in that direction. In Fig., the vertical electric field components are transmitted by the sheet; the horizontal components are absorbed. The transmitted waves are then vertically polarized.

Intensity of Transmitted Polarized Light

We now consider the intensity of light transmitted by a polarizing sheet. We start with unpolarized light, whose electric field oscillations we can resolve into y and z components as represented in this Figure.

Further, we can arrange for the y axis to be parallel to the polarizing direction of the sheet. Then only the y components of the light’s electric field are passed by the sheet; the z components are absorbed. As suggested by Fig., if the original waves are randomly oriented, the sum of the y components and the sum of the z components are equal.

When the z components are absorbed, half the intensity of the original light is lost. The intensity of the emerging polarized light is then

I=12

I 0

Let us call this the one-half rule; we can use it only when the light reaching a polarizing sheet is unpolarized.

Suppose now that the light reaching a polarizing sheet is already polarized.

Figure shows a polarizing sheet in the plane of the page and the electric field of such a polarized light wave traveling toward the sheet. We can resolve the electric field into two components relative to the polarizing direction of the sheet. The parallel component E y is transmitted by the sheet, and perpendicular component E z is absorbed. Since θ is the angle between electric field and the polarizing direction of the sheet, the transmitted parallel component is

E y=E cosθ ……C

Recall that the intensity of an electromagnetic wave (such as our light wave) is proportional to the square of the electric field’s magnitude i.e.

I=E2

rms

c μ0

In our present case then, the intensity I of the emerging wave is proportional to

E2y

and the intensity I 0 of the original wave is proportional to

E2 .

Hence, from Eq. C we can write

II 0

=cos2θ

Or

I=I 0cos2θ

Let us call this the cosine-squared rule; we can use it only when the light reaching a polarizing sheet is already polarized. Then the transmitted intensity I is a maximum and is equal to the original intensity I 0 when the original wave is polarized parallel to the polarizing direction of the sheet. The transmitted intensity is zero when the original wave is polarized perpendicular to the polarizing direction of the sheet.

Two Polarizing Sheets

Figure shows an arrangement in which initially unpolarized light is sent through two polarizing sheets P1 and P2. Often the first sheet is called the polarizer, and the second the analyzer. Because the polarizing direction of P1 is vertical, the light transmitted by P1 to P2 is polarized vertically. If the polarizing direction of P2 is also vertical, then all the light transmitted by P1 is transmitted by P2. If the polarizing direction of P2 is horizontal, none of the light transmitted by P1 is transmitted by P2. We reach the same conclusions by considering only the relative orientations of the two sheets:

If their polarizing directions are parallel, all the light passed by the first sheet is passed by the second sheet (Fig. a).

If those directions are perpendicular (the sheets are said to be crossed), no light is passed by the second sheet (Fig. b).

Finally, if the two polarizing directions of make an angle between 0° and 90°, some of the light transmitted by P1 will be transmitted by P2 , as set by cosine-squared rule.

Other Means of Polarization

Light can be polarized by means other than polarizing sheets, such as by reflection and by scattering from atoms or molecules. In scattering, light that is intercepted by an object, such as a molecule, is sent off in many, perhaps random, directions. An example is the scattering of sun-light by molecules in the atmosphere, which gives the sky its general glow. Although direct sunlight is unpolarized, light from much of the sky is at least partially polarized by such scattering. Bees use the polarization of sky light in navigating to and from their hives. Similarly, the Vikings used it to navigate across the North Sea when the daytime Sun was below the horizon. These early sailors had discovered certain crystals that changed color when rotated in polarized light. By looking at the sky through such a crystal while rotating it about their line of sight, they could locate the hidden Sun and thus determine which way was south.

Conclusion

When a surface intercepts electromagnetic radiation, a force and a pressure are exerted on the surface.

If the radiation is totally absorbed by the surface, the pressure is

P= Sc

The radiation pressure exerted on a perfectly reflecting surface for normal incidence of the wave is

P=2 Sc

Electromagnetic waves are polarized if their electric field vectors are all in a single plane, called the plane of oscillation.

Light waves from common sources are not polarized; that is, they are unpolarized, or polarized randomly.

When a polarizing sheet is placed in the path of light, only electric field components of the light parallel to the sheet’s polarizing direction are transmitted by the sheet; components perpendicular to the polarizing direction are absorbed.

The light that emerges from a polarizing sheet is polarized parallel to the polarizing direction of the sheet.

So friend, that is it for today. See you in the next lecture where we shall talk about reflection and refraction of electromagnetic waves.

Thank you very much.

Course : Bachelor of Applied Physical Science

IInd Year (Semester IV)

Paper no : 14

Subject : PHPT – 404 Electricity, Magnetism and

Electromagnetic Theory

Topic No. & Title : Topic – 1 Electrostatics

Lecture No : 20

Tittle : Polarization

OBJECTIVEThe objective of this lecture is to make the students of B.Sc. Computers understand Polarization of electromagnetic waves.

Course : Bachelor of Applied Physical Science

IInd Year (Semester IV)

Paper no : 14

Subject : PHPT – 404 Electricity, Magnetism and

Electromagnetic Theory

Topic No. & Title : Topic – 1 Electrostatics

Lecture No : 20

Tittle : Polarization

SUMMARYWhen a surface intercepts electromagnetic radiation, a force and a pressure are exerted on the surface.

If the radiation is totally absorbed by the surface, the pressure is

P= Sc

The radiation pressure exerted on a perfectly reflecting surface for normal incidence of the wave is

P=2 Sc

Electromagnetic waves are polarized if their electric field vectors are all in a single plane, called the plane of oscillation.

Light waves from common sources are not polarized; that is, they are unpolarized, or polarized randomly.

When a polarizing sheet is placed in the path of light, only electric field components of the light parallel to the sheet’s polarizing direction are transmitted by the sheet; components perpendicular to the polarizing direction are absorbed.

The light that emerges from a polarizing sheet is polarized parallel to the polarizing direction of the sheet.

Course : Bachelor of Applied Physical Science

IInd Year (Semester IV)

Paper no : 14

Subject : PHPT – 404 Electricity, Magnetism and

Electromagnetic Theory

Topic No. & Title : Topic – 1 Electrostatics

Lecture No : 20

Tittle : Polarization

FAQs Q1. What is polarization of light ?

Ans : Polarization is a property of waves that can oscillate with more than one orientation. Electromagnetic waves, such as light, and gravitational waves exhibit polarization whereas this is not a concern with sound waves in a gas or liquid, which have only one possible polarization, namely the direction in which the wave is travelling.

In an electromagnetic wave such as light, both the electric field and magnetic field are oscillating but in different directions; by convention the "polarization" of light refers to the polarization of the electric field. Light, which can be approximated as a plane wave in free space or in an isotropic medium propagates as a transverse wave—both the electric and magnetic fields are perpendicular to the wave's direction of travel. The oscillation of these fields may be in a single direction (linear polarization), or the field may rotate at the optical frequency (circular or elliptical polarization). In that case the direction of the fields' rotation, and thus the specified polarization, may be either clockwise or counter clockwise; this is referred to as the wave's chirality or handedness.

Polarization is an important parameter in areas of science dealing with transverse wave propagation, such as optics, seismology, radio and microwaves. Especially impacted are technologies such as lasers, wireless and optical fiber telecommunications, and radar.

Q2. What is a Polarizer ?

Ans : A polarizer is an optical filter that passes light of a specific polarization and blocks waves of other polarizations. It can convert a beam of light of undefined or mixed polarization into a beam with well-defined polarization, polarized light. The common types of polarizers are linear polarizers and circular polarizers. Polarizers are used in many optical techniques and instruments, and polarizing filters find applications in photography and liquid crystal display technology. Polarizers can also be made for other types of electromagnetic waves besides light, such as radio waves, microwaves, and X-rays.

Q3. What are-grid Polarizers ?

Ans : The simplest linear polarizer in concept is the wire-grid polarizer, which consists of a regular array of fine parallel metallic wires, placed in a plane perpendicular to the incident beam. Electromagnetic waves which have a component of their electric fields aligned parallel to the wires induce the movement of electrons along the length of the wires. Since the electrons are free to move in this direction, the polarizer behaves in a similar manner to the surface of a metal when reflecting light, and the wave is reflected backwards along the incident beam.

For waves with electric fields perpendicular to the wires, the electrons cannot move very far across the width of each wire; therefore, little energy is reflected, and the incident wave is able to pass through the grid. Since electric field components parallel to the wires are reflected, the transmitted wave has an electric field purely in the direction perpendicular to the wires, and is thus linearly polarized.

For practical use, the separation distance between the wires must be less than the wavelength of the radiation, and the wire width should be a small fraction of this distance. This means that wire-grid polarizers are generally only used for microwaves and for far- and mid-infrared light. Using advanced lithographic techniques, very tight pitch metallic grids can be made which polarize visible light. Since the degree of polarization depends little on wavelength and angle of incidence, they are used for broad-band applications such as projection.

Q4. What is radiation pressure ?

Ans : Radiation pressure is the pressure exerted upon any surface exposed to electromagnetic radiation. Radiation pressure implies an interaction between electromagnetic radiation and bodies of various types, including clouds of particles or gases. The interactions can be absorption, reflection, or some of both (the common case). Bodies also emit radiation and thereby experience a resulting pressure.

The forces generated by radiation pressure are generally too small to be detected under everyday circumstances; however, they do play a crucial role in some settings, such as astronomy and astrodynamics. For example, had the effects of the sun's radiation pressure on the spacecraft of the Viking program been ignored, the spacecraft would have missed Mars orbit by about 15,000 kilometers.

The blue color of the sky is due to

a) Diffraction

b) Reflection

c) Polarization

d) Scattering

Diffraction effect is

a) More for a round edge

b) Less for a round edge

c) More for a sharp edge

d) Less for a sharp edge

The wavelength of X-rays is of the order of

a) 10A

b) 1000A

c) 1A

d) 100A

Light on passing through a Polaroid is

a) Plane polarized

b) Un-polarized

c) Circularly polarized

d) Elliptically polarized

Course : Bachelor of Applied Physical Science

IInd Year (Semester IV)

Paper no : 14

Subject : PHPT – 404 Electricity, Magnetism and

Electromagnetic Theory

Topic No. & Title : Topic – 1 Electrostatics

Lecture No : 20

Tittle : Polarization

GlossaryA wave is disturbance or oscillation that travels through matter/space, accompanied by a transfer of energy.

Gravitational waves are ripples in the curvature of space-time that propagate as a wave, travelling outward from the source.

X-radiation (composed of X-rays) is a form of electromagnetic radiation.

A transverse wave is a moving wave that consists of oscillations occurring perpendicular (or right angled) to the direction of energy transfer.

A plane wave is a constant-frequency wave whose wave fronts (surfaces of constant phase) are infinite parallel planes of constant peak-to-peak amplitude normal to the phase velocity vector.

Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented.

Assignment

At a beach the light is generally partially polarized due to reflections off sand and water. At a particular beach on a particular day near sundown, the horizontal component of the electric field vector is 2.3 times the vertical component. A standing sunbather puts on polarizing sunglasses; the glasses eliminate the horizontal field component. (a) What fraction of the light intensity received before the glasses were put on now reaches the sunbather’s eyes? (b) The sunbather, still wearing the glasses, lies on his side. What fraction of the light intensity received before the glasses were put on now reaches his eyes?

Course : Bachelor of Applied Physical Science

IInd Year (Semester IV)

Paper no : 14

Subject : PHPT – 404 Electricity, Magnetism and

Electromagnetic Theory

Topic No. & Title : Topic – 1 Electrostatics

Lecture No : 20

Tittle : Polarization

References1. Fundamentals of electricity and magnetism By Arthur F. Kip (McGraw-Hill, 1968)2. Electricity and magnetism by J.H.Fewkes & John Yarwood. Vol. I (Oxford Univ. Press, 1991).3. Introduction to Electrodynamics, 3rd edition, by David J. Griffiths, (Benjamin Cummings,1998).4. Electricity and magnetism By Edward M. Purcell (McGraw-Hill Education, 1986)5. Electricity and magnetism. By D C Tayal (Himalaya Publishing House,1988)6. Electromagnetics by Joseph A.Edminister 2nd ed.(New Delhi: Tata Mc Graw Hill, 2006).

Linkshttp://phun.physics.virginia.edu/topics/electrostatics.html

http://www.sciencedirect.com/science/journal/

http://web.mit.edu/8.02t/www/802TEAL3D/visualizations/electrostatics/