<< Chapter < Page
  Waves and optics   Page 1 / 1
Chapter >> Page >
We discuss the polarization of light waves.


Recall that we can add waves so lets take a plane wave traveling in the z direction and break it into components. E x = E 0 x cos ( k z ω t ) ı ̂ E y = E 0 y cos ( k z ω t + δ ) ̂ Where δ is some arbitrary phase between the two components. The electric field for the wave is E = E x + E y Now there are a number of different cases that arise.

If δ = 0 , 2 π , 4 π , Then we can write the field as E = ( E 0 x ı ̂ + E 0 y ̂ ) cos ( k z ω t )

Polarization of light for thecase E = ( E 0 x ı ̂ + E 0 y ̂ ) cos ( k z ω t )

The field is linearly polarized, that is the E field lies along a straight line.

Likewise If δ = π , 3 π , 5 π , Then again it is linearly polarized, but is now "flipped" E = ( E 0 x i ̂ E 0 y j ̂ ) cos ( k z ω t )

Polarization of light for thecase E = ( E 0 x ı ̂ E 0 y ̂ ) cos ( k z ω t )

Circularly polarized light is a particularly interest example. Let δ = π / 2 and E 0 x = E 0 y = E 0

Then E x = E 0 cos ( k z ω t ) ı ̂ E y = E 0 cos ( k z ω t π / 2 ) ̂ E y = E 0 sin ( k z ω t ) ̂ or E = E 0 [ cos ( k z ω t ) ı ̂ + sin ( k z ω t ) ̂ ]

The direction of E is changing with time. For example consider the case at z = 0 . Then

E = E 0 [ cos ( ω t ) ı ̂ + sin ( ω t ) ̂ ]

E = E 0 [ cos ( ω t ) ı ̂ sin ( ω t ) ̂ ]

In this case the electric field undergoes uniform circular rotation. For light coming out of the page, it will have the motion shown in thefigure

Polarization of light for thecase E = E 0 [ cos ( ω t ) ı ̂ sin ( ω t ) ̂ ] . I, and most physicists would call the Left Hand Circular polarization (LHC). The thumb points in thedirection of the light ray and the fingers curve in the direction of rotation. (This is known as the Angular momentum convention, optical scientists will usethe "Optical" convention which is opposite - we will stick to the angular momentum convention.)

Suppose δ = π / 2 then you get E = E 0 [ cos ( k z ω t ) ı ̂ sin ( k z ω t ) ̂ ] This now has the opposite rotation, it is Right Handed.

The most general case of polarization has δ arbitrary and E 0 x E 0 y and is elliptically polarized.


Natural light

Natural light is emitted with the E field in a mixture of random directions. This in unpolarized light. At any particular instant E has a particular direction, but that direction changes rapidly and randomly.

Malus' law

A polarizer is a device that takes incident natural light and transmits polarized light. For example a linear polarizer will take incident light andselect only that component of the light that has its E field lined up along the transmission axis. Suppose there is a linear polarizer that transmits light along a particular axis. This is followed by asecond linear polarizer that has its transmission axis at a different angle with θ being the angle between the transmission axes. Since I E 2 then at the second polarizer I ( θ ) = I ( 0 ) cos 2 θ where I ( 0 ) is the Irradiance of the light hitting the second polarizer.

Lets consider unpolarized light hitting a linear polarizer. Then half the Irradiance will get through. If this is followed by a second polarizer at 90 0 then no light will pass through the second polarizer. Now what happens if a third polarizer is placed between them?

Questions & Answers

what causes demand curve shift to left
Richard Reply
what are the disadvantages of dumping
Edwin Reply
we I don't know
i don't know
what isa microeconomics use for
Favour Reply
what causes demand curve shifted to the left?
what is demand
John Reply
demand is amount of goods and services that a consumer is willing and able to purchase at a giving price over a period of time
demand is some specific thing thats needed by consumer at a certain time
demand is the willingness and ability to demand a particular product at a particular price and at a particular time
demand is an ability and willingness of a consumer to purchase a particular commodity at a given price over a period of time
What does the 45-degree line show
Hassan Reply
the supply line
been unemployed mean s u don't have work whilst been out of labour for means you are not in age of working or you are above the working age (aged)
roy Reply
no, only the working age
Please briefly explain the relationship between the scarcity, choice and opportunity costs
Thandokazi Reply
What is the effect of raising in price to revenue
Michael Reply
what is the difference between inflation and deflation?
price effect
when you increase price, you increase revenue
What are the types of price elasticity of supply
jamilu Reply
What's are the types of elasticity
what is effect of riaising in price to revenue
Shiyghan Reply
consumer consumption will reduce, as well as demand will fall.
what cause inflation
Foday Reply
expenditure on capital goods by the business is known as?
rhandzu Reply
good morning
am new in dis hse
capital expenditure
fundamental of ecnomics
joseph Reply
fu fundamentals of economic problems
Suzan Reply
what are the examples of price elasticity of supply
violet Reply
elastic, inelastic, unitary
Researchers demonstrated that the hippocampus functions in memory processing by creating lesions in the hippocampi of rats, which resulted in ________.
Mapo Reply
The formulation of new memories is sometimes called ________, and the process of bringing up old memories is called ________.
Mapo Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Waves and optics. OpenStax CNX. Nov 17, 2005 Download for free at http://cnx.org/content/col10279/1.33
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Waves and optics' conversation and receive update notifications?