An unpolarized beam of intensity 1-318 W/m2 travels in the positive z-direction

Question

An unpolarized beam of intensity 1-318 W/m2 travels in the positive z-direction and is incident from the left on a series of three linear polarizers as shown. The transmission axis of the first polariner is aligned with the y-axis. The following polarizers make angles of 0-81 degrees, and 8,-29 degrees with the positive x axis. Bad Vine 1) What is l, the intensity of the beam immediately following the second polarizer? W/m 2) What is Ifinals the intensity of the beam immediately following the third polarizer? W/m 3) The positions of the second and third polarizers are now interchanged. What is Iinaan the intensity of the beam after passing through the new arrangement of the three polarizers. W/m2 4) Suppose we now move our incident unpolarized beam so that it is incident from the right. That is, the beam is now incident upon the polarizer whose transmission axis makes an angle 82 with the x- axis and exits the last polarizer (with transmission axis aligned with the y-mis) with intensity ?finalu. How does Ifinal.RI, compare with Ial.new? b a RI-final.new c Ifnal Rd>IinalLnew 5) Suppose we now rotate the last polarizer by 90 degrees so that its transmission axis becomes aligned with the x-axis. With the beam still incident from the right (on the polarizer whose transmission axis makes an angle 02 with the x-axis), what is the Ifinal RI.ncw the intensity of the beam immediately following the last polarizer (transmission axis aligned with the x-axis)? W/m2

Explanation / Answer

given,

Io=318 W/m^2

thet2=81 degrees

theta3=29 degreees

1)

after second polarizer,

intensity, I2=I1*cos^2(90-theta2)

I2=(Io/2)*cos^2(90-theta2)

I2=(318/2)*cos^2(90-81)

I2=155.11 W/m^2

2)

after third polarizer,

intensity, I3=I2*cos^2(theta2-theta3)

I3=(I2)*cos^2(theta2-theta3)

I3=155.11*cos^2(81-29)

I3=58.79 W/m^2

3)

after interchanging the position of the 2nd and 3rd polarizers,

Ifinal,new = I1*cos^2(90-theta3)*cos^2(thet2-theta3)

=(IO/2)*cos^2(90-29)*cos^2(81-29)

=(318/2)*cos^2(90-29)*cos^2(81-29)

=14.165 W/m^2

4)

correct option is (b),

I_final,RL = I_final,new

5)

I_final,RL,new = I1*cos^2(theta1)*cos^2(theta2-theta1)

=(Io/2)*cos^2(29)*cos^2(81-30)

=(318/2)*cos^2(29)*cos^2(81-30)

=48.17 w/m^2

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