The diagram below shows a beam of light shining through three
linear polarizers in a row. The polarizing axis of each polarizer
is measured at an angle (ϴ1,ϴ2,ϴ3) from vertical.
- Suppose that the original beam of light emanates from a vertically polarized laser. The laser has a power output of 1 mW and the beam has a diameter of 2 mm. What is the intensity of the laser beam before it travels through any polarizers?
- Calculate the final intensity of the transmitted beam if ϴ1= 15°, ϴ2 = 40°, and ϴ3 = 82°.
- What would the answer to (b) be if the incident beam were unpolarized, but had the same initial intensity?
- What is the angle of polarization of the light traveling between the second and third polarizers? State your answer as an angle measured from the vertical.
- Now imagine adding a fourth polarizer. At what angle should you orient the axis of the fourth polarizer to completely cancel out the light exiting from the third polarizer? State your answer as an angle measured from the vertical.
Homework Answers
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The diagram below shows a beam of light shining through three linear polarizers in a row. The polarizing axis of each polarizer is measured at an angle (ϴ1,ϴ2,ϴ3) from vertical. Suppose that the orig...
Three polarizing disks whose planes are parallel and centered on common axis. The directions of their...
Three polarizing disks whose
planes are parallel and centered on common axis. The directions of
their transmission axes relative to the vertical are respectively:
θ1 = 37o clockwise, θ2 = 25o counter-clockwise, and θ3 = 18o
clockwise. A beam of light polarized along the vertical is incident
onto the first polarizer with an intensity of I0 = 36.0 W/m².
Calculate the transmitted intensity through all three
polarizers.
7. For each of the three sheets of polarizing material shown in the...
A beam of initially unpolarized light passes through a sequence of three ideal polarizers. The angle...
A beam of initially unpolarized light passes through a sequence of three ideal polarizers. The angle between the axes of the and second polarizers, labeled P12, is 22.1° and the angle between the axes of the second and third polarizers, labeled 023, 53.3°. What is the ratio of the intensity of light emerging from the third polarizer, 13 , to the intensity of light incident on the first polarizer, I ? A beam of unpolarized light shines on a stack...
An optical system consists of a polarizer (polarizing axis at 30o relative to the vertical) and...
An optical system consists of a polarizer (polarizing axis at 30o relative to the vertical) and analyzer (polarizing axis at 75o relative to vertical). 1) When unpolarized light with intensity 60 W/m2 is incident on the polarizer, the transmitted intensity through the whole system is: 15 W/m2 7.5 W/m2 30 W/m2 zero 2) In the above situation, the transmitted light has its polarization axis at an angle relative to the vertical of: 0 degrees 30 degrees 90 degrees 75 degrees...
GOAL Understand how polarizing materials affect light intensity. Unpolarized light is incident upon three polarizers. The...
GOAL Understand how polarizing materials affect light intensity. Unpolarized light is incident upon three polarizers. The first polarizer has a vertical transmission axis, the second has a transmission axis rotated 30.0 degree with respect to the first, and the third has a transmission axis rotated 75.0 degree relative to the first. If the initial light intensity of the beam is I_b, calculate the light intensity after the beam passes through the second polarizer and the third polarizer. After the beam...
law: I = I0 cos²θ where I0 is the intensity of the polarized light beam just before entering the polarizer
law: I = I0 cos²θ where I0 is the intensity of the polarized light beam just before entering the polarizer, I is the intensity of the transmitted light beam immediately after passing through the polarizer, and is the angular difference between the polarization angle of the incident beam and the transmission axis of the polarizer. After passing through the polarizer, the transmitted light is polarized in the direction of the transmission axis of the polarizing filter. Part DOne way to produce a beam of polarized...
What is the intensity I2 of the light after passing through both polarizers?
Learning Goal: To practice Problem Solving Strategy 33.2 Linear Polarization. Unpolarized light of intensity 24 W/cm² is incident on a linear polarizer set at the polarizing angle θ1 = 19°. The emerging light then passes through a second polarizer that is set at the polarizing angleθ1 = 139°. Note that both polarizing angles are measured from the vertical. What is the intensity of the light that emerges from the second polarizer? EXECUTE the solution as follows Part C What is the intensity I2 of the light...
In Figure (a) below, unpolarized light is sent into a system of three polarizing sheets.The angles...
In Figure (a) below, unpolarized light is sent into a
system of three polarizing sheets.The angles
θ1, θ2, and
θ3 of the polarizing directions are measured
counterclockwise from the positive direction of the y axis
(they are not drawn to scale). Angles θ1 and
θ3 are fixed, but angle θ2
can be varied. Figure (b) gives the intensity of the light
emerging from sheet 3 as a function of θ2. (The
scale of the intensity axis is not indicated.) What...
Three polarizing plates whose planes are parallel are centered on a common axis. The directions of...
Three polarizing plates whose planes are parallel are centered
on a common axis. The directions of the transmission axes relative
to the common vertical direction are shown in the figure below. A
linearly polarized beam of light with plane of polarization
parallel to the vertical reference direction is incident from the
left onto the first disk with intensity Ii =
15.0 units (arbitrary). Calculate the transmitted intensity
If when θ1 = 17.0°,
θ2 = 41.0°, and θ3 = 59.0°.
Hint:...
When a beam of light passes through a pair of polarizing filters (polarizer and analyzer), the...
When a beam of light passes through a pair of polarizing filters (polarizer and analyzer), the intensity of the transmitted light is a maximum when the transmission axes of the polarizer and analyzer are parallel to each other (θ = 0° or θ= 180°) and zero when the axes are perpendicular to each other (θ = 90°). For any value of theta between 0° and 90° the transmitted intensity is given by I = Ii cos2(θ) where Ii is the...
Consider three polarizing filters oriented as shown in the figure below. A beam of unpolarized light...
Consider three polarizing filters oriented as shown in the figure below. A beam of unpolarized light is directed through the three filters. The first filter has a polarization axis along the vertical, the second has its polarization axis rotated at an angle of 55° from the vertical, and the third has its axis along the horizontal Polarizer Transmission axis Polarizer Polarizer (a) What fraction of the light intensity comes out of the third filter?
Three polarizing disks whose
planes are parallel and centered on common axis. The directions of
their transmission axes relative to the vertical are respectively:
θ1 = 37o clockwise, θ2 = 25o counter-clockwise, and θ3 = 18o
clockwise. A beam of light polarized along the vertical is incident
onto the first polarizer with an intensity of I0 = 36.0 W/m².
Calculate the transmitted intensity through all three
polarizers.
7. For each of the three sheets of polarizing material shown in the...
A beam of initially unpolarized light passes through a sequence of three ideal polarizers. The angle between the axes of the and second polarizers, labeled P12, is 22.1° and the angle between the axes of the second and third polarizers, labeled 023, 53.3°. What is the ratio of the intensity of light emerging from the third polarizer, 13 , to the intensity of light incident on the first polarizer, I ? A beam of unpolarized light shines on a stack...
GOAL Understand how polarizing materials affect light intensity. Unpolarized light is incident upon three polarizers. The first polarizer has a vertical transmission axis, the second has a transmission axis rotated 30.0 degree with respect to the first, and the third has a transmission axis rotated 75.0 degree relative to the first. If the initial light intensity of the beam is I_b, calculate the light intensity after the beam passes through the second polarizer and the third polarizer. After the beam...
In Figure (a) below, unpolarized light is sent into a
system of three polarizing sheets.The angles
θ1, θ2, and
θ3 of the polarizing directions are measured
counterclockwise from the positive direction of the y axis
(they are not drawn to scale). Angles θ1 and
θ3 are fixed, but angle θ2
can be varied. Figure (b) gives the intensity of the light
emerging from sheet 3 as a function of θ2. (The
scale of the intensity axis is not indicated.) What...
Three polarizing plates whose planes are parallel are centered
on a common axis. The directions of the transmission axes relative
to the common vertical direction are shown in the figure below. A
linearly polarized beam of light with plane of polarization
parallel to the vertical reference direction is incident from the
left onto the first disk with intensity Ii =
15.0 units (arbitrary). Calculate the transmitted intensity
If when θ1 = 17.0°,
θ2 = 41.0°, and θ3 = 59.0°.
Hint:...
Consider three polarizing filters oriented as shown in the figure below. A beam of unpolarized light is directed through the three filters. The first filter has a polarization axis along the vertical, the second has its polarization axis rotated at an angle of 55° from the vertical, and the third has its axis along the horizontal Polarizer Transmission axis Polarizer Polarizer (a) What fraction of the light intensity comes out of the third filter?
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