A linearly polarized beam of light of intensityI0 is propagating in the +z direction and its direction of polarization makes an angle of 74° with the x-axis (the angle between the initial direction of polarization and the transmission axis of the first polarizer is 16° as described below). Two linear polarizing sheets are lined up perpendicular to the beam. The first sheet has its transmission axis at an angle q 1 = 90° with respect to thex-axis. The transmission axis of the second is variable. (See lower panels of the figure.)
(a) Calculate the intensity I1 of the light after it has passed through the first polarizer. Express your answer as a fraction of I0.
(b) Calculate the electric field amplitudeE1 of the light after it has passed through the first polarizer. Express your answer as a fraction of the electric field amplitude E0 of the initial beam.
(c) The second polarizer is set at various angles within the rangeq 2 = 0 to 90°.Calculate the intensity of the light after it has passed through thesecond polarizer for the following values of q 2. Express each answer as a fractionof I1.
At q 2 = 0°: I2 / I1 =
At q 2 = 30°: I2 / I1 =
At q 2 =
90°: I2 /
I1 = 
Homework Answers
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A linearly polarized beam of light of intensityI0 is propagating
in the +z direction and its...
A linearly polarized beam of light of intensityI0 is propagating in the +z directionand...
A linearly polarized beam of light of intensityI0 is propagating in the +z direction and its direction of polarization makes an angle of 64° with the x-axis (the angle between the initial direction of polarization and the transmission axis of the first polarizer is 26° as described below). Two linear polarizing sheets are lined up perpendicular to the beam. The first sheet has its transmission axis at an angleθ1 = 90° with respect to the x-axis. The transmission axis of...
To understand polarization of light and how to use Malus's law to calculate the intensity of...
To understand polarization of light and how to use Malus's law to calculate the intensity of a beam of light after passing through one or more polarizing filters. The two transverse waves shown in the figure(Figure 1) both travel in the +z direction. The waves differ in that the top wave oscillates horizontally and the bottom wave oscillates vertically. The direction of oscillation of a wave is called the polarization of the wave. The upper wave is described as polarized...
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...
A beam of polarized light has an average intensity of 15 W/m2 and is sent through...
A beam of polarized light has an average intensity of 15 W/m2 and is sent through a polarizer. The transmission axis makes an angle of 34° with respect to the direction of polarization. Determine the rms value of the electric field of the transmitted beam.
A beam of light is polarized all along the y-axis, and passes through a polarizer that...
A beam of light is polarized all along the y-axis, and passes through a polarizer that has its polarization axis 45° from the y-axis. 1) What fraction of the original electric field amplitude E0 makes it through the polarizer? What direction is it now polarized in? 2) Knowing that the intensity of light is proportional to the square of the amplitude of the electric field, what fraction of the original intensity I0 makes it through the polarizer?
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...
A beam of polarized light with an average intensity of 12.5 W/m² is sent through a...
A beam of polarized light with an average intensity of 12.5 W/m² is sent through a polarizer. The transmission axis makes an angle of 22.0° with respect to the direction of polarization. Determine the rms value of the magnetic field of the transmitted beam.
Linearly polarized light propagating along the y-direction is incident on a polarizer whose axis is parallel...
Linearly polarized light propagating along the y-direction is incident on a polarizer whose axis is parallel to the 2-direction. If the intensity of the transmitted light is equal to 33% of the incident intensity, what is the angle of polarization (in degrees) between the incident light and the z-axis? (Insert the number of degrees without unit)
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?
A beam of unpolarized light with intensity I 0 falls first upon a polarizer with transmission...
A beam of unpolarized light with intensity I 0 falls first
upon a polarizer with transmission axis theta TA,1 then upon a
second polarizer with transmission axis theta TA.2 where theta TA,2
- theta TA,1 =90 degrees in other words the two axes are
perpendicular to one another) What is the intensity I 2 of the
light beam emerging from the second polarizer? ( Figure 4) Express
your answer as a decimal number times the symbol I 0 For example,...
Linearly polarized light propagating along the y-direction is incident on a polarizer whose axis is parallel to the 2-direction. If the intensity of the transmitted light is equal to 33% of the incident intensity, what is the angle of polarization (in degrees) between the incident light and the z-axis? (Insert the number of degrees without unit)
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?
A beam of unpolarized light with intensity I 0 falls first
upon a polarizer with transmission axis theta TA,1 then upon a
second polarizer with transmission axis theta TA.2 where theta TA,2
- theta TA,1 =90 degrees in other words the two axes are
perpendicular to one another) What is the intensity I 2 of the
light beam emerging from the second polarizer? ( Figure 4) Express
your answer as a decimal number times the symbol I 0 For example,...
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