The graph shows the intensity of light as a function of position. The light is e

Question

The graph shows the intensity of light as a function of position. The light is emitted from a laser at x 500 W/m2.) 0 cm, with an initial intensity of 840 w m. That is not shown on the graph, seeing as the graph only goes to I (W m2) light intensity as a function of position 400 300 200 100 x (cm) 10 20 30 40 50 The light then passes through a sequence of five polarizers. Polarizer 1 is at the 10 cm mark, polarizer 2 at the 20 cm mark, polarizer 3 at the 30 cm mark, polarizer 4 at the 40 cm mark, and polarizer 5 at the 50 cm mark. The intensity after 50 cm is also not shown-you have to figure that out. Note that the transmission axis of each polarizer is an angle between 0 degrees and 90 degrees, and the angle of any polarizer is always greater than or equal to the angle of the one immediately before it. Polarizer 1 is at an angle of 0 degrees. (a) The light emitted by the laser is linearly polarized-at what angle? (The angle is between 0 and 90 degrees.) 46.4 degrees (b) Choose all the correct statements about this situation from the list below If you rotated polarizer 1 a few degrees, so its transmission axis was closer to your answer to (a), only the intensity of the light between 10 and 20 cm would increase-the ones beyond that would stay the same If you rotated polarizer 1 a few degrees, so its transmission axis was closer to your answer to (a), the intensity of the light in all sections (10 cm-50 cm) of the graph above would increase. Removing polarizer 2 completely would have no effect at all on the graph above. Removing polarizer 3 completely would have no effect at all on the graph above. If you remove both polarizer 2 and polarizer 3, the intensity of the light between x 40 cm and x = 50 cm would increase. 0 If you remove both polarizer 2 and polerizer 3, the intensity of the light between x 40 cm and x = 50 cm would stay the same. If you remove both polarizer 2 and polarizer 3, the intensity of the light between x = 40 cm and x = 50 cm would decrease. (c) Note that you should be able to figure out the angles of polarizers 2, 3, and 4. The angle of polarizer 5 is 89 degrees. The intensity of the light emerging from polarizer 4 is 150 W/m2. What is the intensity of the light after x50 cm? 75 (d) Now, we change things up. The laser is set so the polarization direction of the light is 40 degrees. Polarizer 1 is still set at 0 degrees, and polarizer 5 is set to 90 degrees. The other three polarizers you can set to whatever angles you want. What is the maximum intensity you can achieve for the light that emerges from polarizer 5? W/m2

Explanation / Answer

part c:

let angle between polarizer 1 and polarizer 2 be theta.

using Malus’ law:

output of polarizer 1=input of polarizer 1*cos^2(theta)

==>300=400*cos^2(theta)

==>theta=30 degrees

so angle of polarizer 2 is 30 degrees

let angle between polarizer 2 and polarizer 3 be theta.

using Malus’ law:

output of polarizer 2=input of polarizer 2*cos^2(theta)

==>300=300*cos^2(theta)

==>theta=0 degrees

so angle of polarizer 3 is 30 degrees

let angle between polarizer 3 and polarizer 4 be theta.

using Malus’ law:

output of polarizer 3=input of polarizer 4*cos^2(theta)

==>150=300*cos^2(theta)

==>theta=45 degrees

so angle of polarizer 4 is 30+45=75 degrees

angle between polarizer 4 and 5 =89-75=14 degrees

then intensity of light after x=50 cm=output of polrizer 5

=input of polarizer 5*cos^(14)

=141.22 W/m^2

part d:

intensity output from polarizer 1=840*cos^2(40)=492.93 W/m^2

setting all others to 0 degrees , input intensity to polarizer 5=492.93 W/m^2

angle=90-40=50 degrees

then

intensity output of polarizer 5=492.93*cos^2(50)=203.67 W/m^2

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