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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
If auger is pair are the roots of equation x2+5x-3=0
Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.
from theory: distance [miles] = speed [mph] × time [hours]
info #1
speed_Dennis × 1.5 = speed_Wayne × 2
=> speed_Wayne = 0.75 × speed_Dennis (i)
info #2
speed_Dennis = speed_Wayne + 7 [mph] (ii)
use (i) in (ii) => [...]
speed_Dennis = 28 mph
speed_Wayne = 21 mph
George
Let W be Wayne's speed in miles per hour and D be Dennis's speed in miles per hour. We know that W + 7 = D and W * 2 = D * 1.5.
Substituting the first equation into the second:
W * 2 = (W + 7) * 1.5
W * 2 = W * 1.5 + 7 * 1.5
0.5 * W = 7 * 1.5
W = 7 * 3 or 21
W is 21
D = W + 7
D = 21 + 7
D = 28
Salma
Devon is 32 32 years older than his son, Milan. The sum of both their ages is 54 54. Using the variables d d and m m to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.
find product (-6m+6) ( 3m²+4m-3)
what is the solution
bill
how did you arrive at this answer?
bill
i really want to learn
Amira
I only got 42 the rest i don't know how to solve it. Please i need help from anyone to help me improve my solving mathematics please
Amira
Hw did u arrive to this answer.
Aphelele
-6m(3mA²+4m-3)+6(3mA²+4m-3)
=-18m²A²-24m²+18m+18mA²+24m-18
Rearrange like items
-18m²A²-24m²+42m+18A²-18
Salma
complete the table of valuesfor each given equatio then graph.
1.x+2y=3
given that (7x-5):(2+4x)=8:7find the value of x
Nandala
please why isn't that the 0is in ten thousand place
please why is it that the 0is in the place of ten thousand
Grace
Send the example to me here and let me see
Stephen
A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of one of the other legs. Find the lengths of the hypotenuse and the other leg
state in which quadrant or on which axis each of the following angles given measure. in standard position would lie 89°
I am eliacin, I need your help in maths
Rood
hmm can we speak here?
Amoon
however, may I ask you some questions about Algarba?
Amoon
what the last part of the problem mean?
Roger
The Jones family took a 15 mile canoe ride down the Indian River in three hours. After lunch, the return trip back up the river took five hours. Find the rate, in mph, of the canoe in still water and the rate of the current.
Shakir works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925.
I'm guessing, but it's somewhere around $4335.00 I think
Lewis
12% of sales will need to exceed 925 - 500, or 425 to exceed fixed amount option. What amount of sales does that equal? 425 ÷ (12÷100) = 3541.67. So the answer is sales greater than 3541.67.
Check:
Sales = 3542
Commission 12%=425.04
Pay = 500 + 425.04 = 925.04.
925.04 > 925.00
Munster
difference between rational and irrational numbers
When traveling to Great Britain, Bethany exchanged $602 US dollars into £515 British pounds. How many pounds did she receive for each US dollar?
how to reduced echelon form
Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?
d=r×t
the equation would be 8/r+24/r+4=3
worked out
Sheirtina
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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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