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A beam of polarized light passes through a polarizing filter. When the angle between the polarizing axis of the filter and the direction of polarization of the light is \theta, the intensity of the emerging beam is I.

If you now want the intensity to be I/2, what should be the angle (in terms of \theta) between the polarizing angle of the filter and the original direction of polarization of the light?

Express your answer in terms of the given variable.

alpha = ???

I understand that the angle must be 45 degrees but I have no clue on how to find alpha. Any help is appreciated! Thanks!!

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Added Fri, 07 Aug '15
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I = Io*cos^2(theta) ---(1)

I/2 = Io*cos^2(alfa) ---(2)

(2)/(1) ==> 1/2 = cos^2(alfa)/cos^2(theta)

1/sqrt(2) = cos(alfa)/cos(theta)

cos(alfa) = cos(theta)*1/sqrt(2)

==> alfa = cos^-1(cos(theta)/sqrt(2))
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Added Fri, 07 Aug '15
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