On the extreme left is a light source issuing polarized light of amplitude \'Ao\

Question

On the extreme left is a light source issuing polarized light of amplitude 'Ao' and being projected to the right. This light passes through a first polarizer immediately to the right of the source. The angle between the polarization direction and the first polarizer's axis is theta. Just past the first polarizer to its right, is a second light source that is also issuing polarized light of amplitude 'Ao' projected to its right. the polarization direction of this second source is parallel to the first polarizer's axis. Just past the second light source to its right is a second polarizer with its axis at an angle '2*theta' relative to the first sources axis. Assuming that the wave trains from the two sources 'mesh', if the net light amplitude exiting the second polarizer is '.25*Ao', determine the angle theta.

Explanation / Answer

intensity of light from first polarizer = I1 = Io*(cos(theta))^2

I1/Io = A1^2/Ao^2

A1 = Ao*cos(theta)

amplitude of the wave falling on second polarizer = A2 = A1+Ao = Ao*(1+cos(theta))

intensity of light coming from second polarizer = I3 = I2*cos(2theta)^2)

I3/I2 = A3^2/A2^2

A3 = A2*cos(2theta)

A3 = 0.25 Ao

A2 = Ao*(1+cos(theta))

0.25*Ao = Ao*(1+cos(theta))*cos(2theta)

0.25 = (1 + cos(theta))*cos(2theta)

theta = 40.9 degees

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