In the figure on the left below, unpolarized light is sent through a system of t

Question

In the figure on the left below, unpolarized light is sent through a system of three polarizing sheets. The angles ?1, ?2, and ?3 of the polarizing axes of the sheets are measured counterclockwise from the positive direction of the y axis (they are not drawn to scale). Angles ?1 and ?3 are fixed but angle ?2 can be varied. The figure on the right gives the intensity of the light emerging from sheet 3 as a function of ?2. (The scale of the intensity axis is not indicated.) What percentage of the light's initial intensity is transmitted by the three-sheet system when ?2 = 90

Explanation / Answer

Iout/Iin=.5*cos(theta2-theta 1)^2*cos(theta3-theta 2)^2

when theta2=60 no light pases that is axis of 2 becomes perpendicular to 1 thus theta1+ 60=90 gives theta1=-30

and when theta2= 140 no light passes that is axis of 2 becomes perpendicular to 3 theta3-theta2=90 gives theta 3=230

thus when theta 2=90

Iout/Iin=.5*cos(theta2-theta 1)^2*cos(theta3-theta 2)^2=.5*cos(120)^2*cos(140)^2

percentage=Iout/in *100 =7.3353 %

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