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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 , the intensity of the emerging beam is I.

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

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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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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