Three polarizers are arranged as shown below. What fraction (if any) of the orig

Question

Three polarizers are arranged as shown below. What fraction (if any) of the original unpolarized light intensity is transmitted through the combination? Is light transmitted if the middle polarizer is rotated counterclockwise by 45 degree making it a vertical polarizer? What about if it is rotated clockwise by 45 degree making a horizontal polarizer? Explain your answers. Apply 900v to the Geiger tube, set the Preset Time to 60 seconds. Place the radioactive source in the top shelf (2 cm from the detector) Collect the count. Move the source down (Shelfs separated by 1 cm) and take another point. Continue to the lower shelfs. Record the data in the provided table. Neglect the background. Graph the count dependence on the source distance from the GM probe. Explain your result.

Explanation / Answer

Consider the intensity of the incident beam is I0

After first polarizer, Intensity = I0/2

After second polarizer, Intensity =  I0 Cos(45)/2 = I0/(2*sqrt(2))

After third polarizer, Intensity = I0 Cos(45)/(2*sqrt(2)) = I0/(2*sqrt(2)*sqrt(2)) = I0/4.

When the middle polarizer is rotated counter-clockwise by 45 degree making it a vertical polarizer, the light will be transmitted. The reason being that the first polarizer will make the beam vertically polarized and the it will pass completely if the second polarizer is vertically orriented.

When the middle polarizer is rotated clockwise by 45 degree making it a horizontal polarizer, the light will not be transmitted. The reason being that the first polarizer will make the beam vertically polarized and the it will not pass if the second polarizer is horizontally orriented.

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