Physics for Scientists and Engineers 7th step-by-step solutions:Chapter 38 Problem 40P

Question

Suppose the transmission axes of the left and right polarizingdisks are perpendicular to each other. Also, let the center disk berotated on the common axis with an angular speed . Showthat if unpolarized light is incident on the left disk with anintensity Imax, the intensity of the beam energing fromthe right disk is
I = (1/16)Imax(1 - cos4t)
I promise to rate you aslifesaver if your answer is correct! Suppose the transmission axes of the left and right polarizingdisks are perpendicular to each other. Also, let the center disk berotated on the common axis with an angular speed . Showthat if unpolarized light is incident on the left disk with anintensity Imax, the intensity of the beam energing fromthe right disk is
I = (1/16)Imax(1 - cos4t)
I promise to rate you aslifesaver if your answer is correct!

Explanation / Answer

   for the incident unpolarized light ofintensity Imax    after transmitting through the first disk I= (1 / 2) Imax    after transmitting through the second disk I= (1 / 2) Imax cos2    after transmitting through the thirddisk I = (1 / 2) Imaxcos2cos2(90o - )    where the angle between the first and thesecond disk will be = t    using the trignometric identities    cos2 = (1 / 2) (1 +cos2)    cos2(90o - ) =sin2                         = (1 / 2) (1 - cos2)     we have I = (1 / 2) Imax [(1 +cos2) / 2][(1 - cos2) / 2]    I = (1 / 8) Imax (1 -cos22)      = (1 / 8) Imax (1 /2) (1 - cos4)    as = t    the intensity of the emerging beam is givenby    I = (1 / 16) Imax (1 - 4 t)

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