# 7.8 Polarization  (Page 7/19)

 Page 7 / 19

Can a sound wave in air be polarized? Explain.

No light passes through two perfect polarizing filters with perpendicular axes. However, if a third polarizing filter is placed between the original two, some light can pass. Why is this? Under what circumstances does most of the light pass?

Explain what happens to the energy carried by light that it is dimmed by passing it through two crossed polarizing filters.

When particles scattering light are much smaller than its wavelength, the amount of scattering is proportional to $1/{\lambda }^{4}$ . Does this mean there is more scattering for small $\lambda$ than large $\lambda$ ? How does this relate to the fact that the sky is blue?

Using the information given in the preceding question, explain why sunsets are red.

When light is reflected at Brewster’s angle from a smooth surface, it is $\text{100%}\text{}$ polarized parallel to the surface. Part of the light will be refracted into the surface. Describe how you would do an experiment to determine the polarization of the refracted light. What direction would you expect the polarization to have and would you expect it to be $\text{100%}\text{}$ ?

## Problems&Exercises

What angle is needed between the direction of polarized light and the axis of a polarizing filter to cut its intensity in half?

$\text{45}\text{.}0º$

The angle between the axes of two polarizing filters is $\text{45}\text{.}0º$ . By how much does the second filter reduce the intensity of the light coming through the first?

If you have completely polarized light of intensity $\text{150 W}/{\text{m}}^{2}$ , what will its intensity be after passing through a polarizing filter with its axis at an $\text{89}\text{.}0º$ angle to the light’s polarization direction?

$\text{45}\text{.}7\phantom{\rule{0.25em}{0ex}}{\text{mW/m}}^{2}$

What angle would the axis of a polarizing filter need to make with the direction of polarized light of intensity $1\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}{\text{kW/m}}^{2}$ to reduce the intensity to $10\text{.}0\phantom{\rule{0.25em}{0ex}}{\text{W/m}}^{2}$ ?

At the end of [link] , it was stated that the intensity of polarized light is reduced to $\text{90}\text{.}0%\text{}$ of its original value by passing through a polarizing filter with its axis at an angle of $\text{18}\text{.}4º$ to the direction of polarization. Verify this statement.

$\text{90}\text{.}0%\text{}$

Show that if you have three polarizing filters, with the second at an angle of $\text{45º}$ to the first and the third at an angle of $\text{90}\text{.}0º$ to the first, the intensity of light passed by the first will be reduced to $\text{25}\text{.}0%\text{}$ of its value. (This is in contrast to having only the first and third, which reduces the intensity to zero, so that placing the second between them increases the intensity of the transmitted light.)

Prove that, if $I$ is the intensity of light transmitted by two polarizing filters with axes at an angle $\theta$ and $I\prime$ is the intensity when the axes are at an angle $\text{90.0º}-\mathrm{\theta ,}$ then $I+I\prime ={I}_{0,}$ the original intensity. (Hint: Use the trigonometric identities $\text{cos}\phantom{\rule{0.25em}{0ex}}\left(90.0º-\theta \right)=\text{sin}\phantom{\rule{0.25em}{0ex}}\theta$ and ${\text{cos}}^{2}\phantom{\rule{0.25em}{0ex}}\theta +{\text{sin}}^{2}\phantom{\rule{0.25em}{0ex}}\theta =1.$ )

${I}_{0}$

At what angle will light reflected from diamond be completely polarized?

What is Brewster’s angle for light traveling in water that is reflected from crown glass?

$\text{48}\text{.}8º$

A scuba diver sees light reflected from the water’s surface. At what angle will this light be completely polarized?

At what angle is light inside crown glass completely polarized when reflected from water, as in a fish tank?

$\text{41}\text{.}2º$

Light reflected at $\text{55}\text{.}6º$ from a window is completely polarized. What is the window’s index of refraction and the likely substance of which it is made?

(a) Light reflected at $\text{62}\text{.}5º$ from a gemstone in a ring is completely polarized. Can the gem be a diamond? (b) At what angle would the light be completely polarized if the gem was in water?

(a) 1.92, not diamond (Zircon)

(b) $\text{55}\text{.}2º$

If ${\theta }_{\text{b}}$ is Brewster’s angle for light reflected from the top of an interface between two substances, and ${\theta \prime }_{\text{b}}$ is Brewster’s angle for light reflected from below, prove that ${\theta }_{\text{b}}+{\theta \prime }_{\text{b}}=\text{90}\text{.}0º.$

Integrated Concepts

If a polarizing filter reduces the intensity of polarized light to $\text{50}\text{.}0%\text{}$ of its original value, by how much are the electric and magnetic fields reduced?

${B}_{2}=0\text{.}\text{707}\phantom{\rule{0.25em}{0ex}}{B}_{1}$

Integrated Concepts

Suppose you put on two pairs of Polaroid sunglasses with their axes at an angle of $\text{15}\text{.}0º$ . How much longer will it take the light to deposit a given amount of energy in your eye compared with a single pair of sunglasses? Assume the lenses are clear except for their polarizing characteristics.

Integrated Concepts

(a) On a day when the intensity of sunlight is $1\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{kW}/{\text{m}}^{2}$ , a circular lens 0.200 m in diameter focuses light onto water in a black beaker. Two polarizing sheets of plastic are placed in front of the lens with their axes at an angle of $\text{20}\text{.}0º.$ Assuming the sunlight is unpolarized and the polarizers are $\text{100%}\text{}$ efficient, what is the initial rate of heating of the water in $\text{ºC}/\text{s}$ , assuming it is $\text{80}\text{.}0%\text{}$ absorbed? The aluminum beaker has a mass of 30.0 grams and contains 250 grams of water. (b) Do the polarizing filters get hot? Explain.

(a) $2.07×{10}^{-2}$ °C/s

(b) Yes, the polarizing filters get hot because they absorb some of the lost energy from the sunlight.

how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Got questions? Join the online conversation and get instant answers!