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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?
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When particles scattering light are much smaller than its wavelength, the amount of scattering is proportional to
. Does this mean there is more scattering for small
than large
? How does this relate to the fact that the sky is blue?
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When light is reflected at Brewster’s angle from a smooth surface, it is
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
?
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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?
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The angle between the axes of two polarizing filters is
. By how much does the second filter reduce the intensity of the light coming through the first?
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If you have completely polarized light of intensity
, what will its intensity be after passing through a polarizing filter with its axis at an
angle to the light’s polarization direction?
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What angle would the axis of a polarizing filter need to make with the direction of polarized light of intensity
to reduce the intensity to
?
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At the end of
[link] , it was stated that the intensity of polarized light is reduced to
of its original value by passing through a polarizing filter with its axis at an angle of
to the direction of polarization. Verify this statement.
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Show that if you have three polarizing filters, with the second at an angle of
to the first and the third at an angle of
to the first, the intensity of light passed by the first will be reduced to
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.)
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Prove that, if
is the intensity of light transmitted by two polarizing filters with axes at an angle
and
is the intensity when the axes are at an angle
then
the original intensity. (Hint: Use the trigonometric identities
and
)
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Light reflected at
from a window is completely polarized. What is the window’s index of refraction and the likely substance of which it is made?
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(a) Light reflected at
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)
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If
is Brewster’s angle for light reflected from the top of an interface between two substances, and
is Brewster’s angle for light reflected from below, prove that
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Integrated Concepts
If a polarizing filter reduces the intensity of polarized light to
of its original value, by how much are the electric and magnetic fields reduced?
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Integrated Concepts
Suppose you put on two pairs of Polaroid sunglasses with their axes at an angle of
. 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.
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Integrated Concepts
(a) On a day when the intensity of sunlight is
, 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
Assuming the sunlight is unpolarized and the polarizers are
efficient, what is the initial rate of heating of the water in
, assuming it is
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)
°C/s
(b) Yes, the polarizing filters get hot because they absorb some of the lost energy from the sunlight.
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Questions & Answers
differentiate between demand and supply
giving examples
differentiated between demand and supply using examples
Lambiv
how is the graph works?I don't fully understand
hi guys good evening to all
Lambiv
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
Ezea
other things being equal
AI-Robot
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Kelo
Can I ask you other question?
Shukri
What is different between quantity demand and demand?
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
how do you save a country economic situation when it's falling apart
what is the difference between economic growth and development
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
any question about economics?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has
The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50.
A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
C,Calculate quantities of X and Y consumed with a given price.
D,alculate optimum level of output .
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
Abdureman
What is the difference between perfect competition and monopolistic competition?
Mohammed
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Source:
OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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