Lecture15 Polarization

7/21/2019 Lecture15 Polarization

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Chapter 24

ElectromagneticWaves


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24.6 Polarization

A transverse wave is linearly polarized

when its vibrations always occur along

one direction.

A linearly polarized wave on a rope

canpass through a slit that is parallel

to the direction of the rope vibrations.

The rope wave cannotpass througha slit that is perpendicular tothe

vibrations.

POLARIZED ELECTROMAGNETIC WAVES


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24.6 Polarization

In polarized light, the electric field

of the electromagnetic wave fluctuates

along a single direction.

Unpolarized lightconsists of short

bursts of electromagnetic waves emitted

by many different atoms. The electricfield directions of these bursts are

perpendicular to the direction of wave

travel, as in polarized light, but are

distributed randomly about it.


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24.6 Polarization

Polarized light may be produced from unpolarized light with the aid of

polarizing material.

The intensity of the transmitted polarized light has 1/2 the intensity of

the incident unpolarized light (perpendicular component blocked).

The transmission axis of the material is the direction of polarization

of the light that passes through the material.


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24.6 Polarization

MALUS

LAW !2

coso

SS =

intensity beforeanalyzer

intensity after

analyzer

Consider two sheets of polarizing material, one to polarize unpolarized light

(Polarizer) and one at an angle !to the polarized light (Analyzer). The

intensity of the light after the analyzer is related to the intensity before the

analyzer by Malus

Law:

( Intensity ~ E2)


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24.6 Polarization

Example 7 Using Polarizers and Analyzers

What value of !should be used so the average intensity of the polarized

light reaching the photocell is one-tenththe average intensity of the

unpolarized light?


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24.6 Polarization

!2

5

1cos=

5

1cos =! !

4.63=!

Applying MalusLaw at the Analyzer: S= S0,polarcos2!

But S0,polar= (1/2)S0 and we want S= (1/10)S0

So (1/10)S0= (1/2)S0cos2

!

S0 S0,polar S

! !


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24.6 Polarization

Conceptual Example 8 How Can a Crossed Polarizer and

Analyzer Transmit Light?

Suppose that a third piece of polarizing material is inserted between the

crossed polarizer and analyzer. Does light now reach the photocell?

S0 S1 S2 S3

S1= S0/2

S2= S1cos2!

= (S0/2) cos2!

S3= S2cos2(90 - !)

= (S0/2) cos2!sin2!

Clearly, S3> 0 as long as

!!0 or 90o


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24.6 Polarization

Polarized light is produced by the scattering of unpolarized

sunlight by molecules in the atmosphere.

Molecules re-radiate sunlight.

As you look at larger and larger

angles with respect to the

incident sunlight, the re-radiated

light becomes more and more

horizontally polarized.


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Polaroid Sun Glasses

Besides sunlight re-radiated from atmospheric molecules, there are

other sources of horizontally polarizedlight that occur in nature, such

as sunlight reflected from horizontal surfaces such as lakes.

Polaroid sun glassestake advantage of this fact by using polarizers

with their axes oriented vertically:

!in addition to 1/2 of the unpolarized light which is already blocked by

the polarizers, all of the horizontally polarized light is completely blocked,

thus blocking out some of the reflected light which can confuse you

during some outdoor activities (e.g. driving, piloting, fishing!!.).


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24.6 Polarization

IMAX movie projector Movie viewer using polarized glasses

Another application using polarized glasses: watching 3-D movies.

In a 3-D movie, two separate rolls of film are projected using a projectorwith two lenses, each with its own polarizer. The two polarizers are

crossed. Viewers watch the action on-screen through glasses that have

correspondingly crossed polarizers for each eye.


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Example. Partially polarized and partially unpolarized light.

A light beam passes through a polarizer whose transmission axis makes

angle !with the vertical. The beam is partially polarized and

partially unpolarized, and the average intensity of the incident light,

S0, is the sum of the average intensity of the polarized light, S0,polar,

and the average intensity of the unpolarized light, S0,unpolar.

As the polarizer is rotated clockwise, the intensity of the transmitted light

has a minimum value of 2.0 W/m2when != 20.0oand has a maximum

value of 8.0 W/m2when the angle is != !max.

!Find a) S0,unpolar, and b) S0,polar.

Incident light

S0= S0,polar+ S0,unpolar

Transmitted light

S= Spolar+ Sunpolar


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Incident lightS0= S0,polar+ S0,unpolarTransmitted lightS= Spolar+ Sunpolar

a) Minimum transmitted intensity S= Smin= 2.0 W/m2at != 20.0o.

Sis minimum when Spolar= 0 since Sunpolaris not effected by !.

Sunpolar= Smin- Spolar= 2.0 - 0 = 2.0 W/m2

Sunpolar= (1/2)S0,unpolar ! S0,unpolar= 2Sunpolar= 2(2.0) = 4.0 W/m2

b) Maximum transmitted intensity S= Smax= 8.0 W/m2occurs at !max.

Sis maximum when Spolar= S0,polar(when != 20o+ 90o= 110o= !max)

Smax= S0,polar+ Sunpolor!S0,polar= Smax- Sunpolar= 8.0 - 2.0 = 6.0 W/m2

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Lecture15 Polarization