A monochromatic laser beam of intensity 1,- 560 W/m2 is polarized in the propaga

Question

A monochromatic laser beam of intensity 1,- 560 W/m2 is polarized in the propagates in the positive z-direction. This beam is incident upon a makes an angle of 45 degrees with the x-axis as shown. Following the polarizers; the transmission axis of the first polarizer is aligned with axis of the and ind quarter-wave plate whose fast axis quarter-wave plate are two the x-axis, while the transmison second polarizer makes an angle of 0, -77 degrees with the positive x axis. Side Viw Polarized along y End Viaw 7) What is Imid, the intensity of the beam immediately following the polarizer whose transmission axis is aligned with the x-axis? W/m2 8) What is Isinal the intensity of the beam immediately following the last polarizer? W/m 9) What is the ratio of Ey,tinal, the maximum value of the y-component of the electric field immediately following the last polarizer, to Fo, the amplitude of the electric field oscillations in the incident polarized beam? 10) The positions of the quarter-waveplate and the last polarizer are now interchanged. What is fanew the intensity of the beam after passing through the new arrangement of the two polarizers and the quarter-wave plate? Side Vine Polarized along y ay ya End View W/m

Explanation / Answer

Io=560 W/m^2

theta=45 degrees

theta1=77 degrees

a)

I_mid=Io*cos^2(theta)

I_mid=560*cos^2(45)

I_mid=280 W/m^2

b)

I_final=I_mid*cos^2(theta1)

=280*cos^2(77)

=14.17 W/m^2

c)

Ey,final/Eo = sqrt(I_final*sin^2(theta1)/IO)

Ey,final/Eo = sqrt(14.17*sin^2(77)/560)

Ey,final/Eo = 0.155

d)

I=Io*cos^2(theta1)*cos^2(90-theta1)

=560*cos^2(77)*cos^2(90-77)

=26.904 w/m^2

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