The following are positioned in sequence: A source of beam of natural light inte

Question

The following are positioned in sequence: A source of beam of natural light
intensity Io; three ideal polarizers A, B, and C; and an observer. Polarizer axis angles are measured clockwise from the vertical, from the perspective of the observer. The axis of polarizer A is set at zero degrees (vertical), and the axis angle of polarizer C is set at 50 degrees. (a) If polarizer B is set so the beam intensity is zero at the observer, what are the two possible axis angel settings of polarizer B?

If polarizer B is set so that the beam intensity at the observer is a maximum, what is the axis angle of polarizer B? (c) If the axis angle of polarizer B is set to 120o, what is the ratio of the intensity of the beam at the observer to the intensity of the source?

Explanation / Answer

let theta be angle of B

a) then I = I0 x 1/2 x cos2(theta) x cos2(theta-50) = 0

theta = 90 or theta = 140

b) I = I0 x 1/2 x cos2(theta) x cos2(theta-50) = maximum

  cos2(theta) x cos2(theta-50) = maximum

cos(theta) x cos(theta-50) = maximum

theta = 25

c)  I = I0 x 1/2 x cos2(120) x cos2(120-50) = 0.014622 I0

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