Three polarizing plates whose planes are paralel are centered on a common axis.

Question

Three polarizing plates whose planes are paralel are centered on a common axis. The directions of the transmission axes relative to the common vertical direction are shown in the figure below. A linearly polarized beam of light with plane of polarization parallel to the vertical reference direction is incident from the left onto the first disk with intensity I 14.0 units (arbitrary). Calculate the transmitted intensity If when 17.09, ?2-44.0°, and 03-58.0. (Hint: Make repeated use of Malus's law. Ir- units

Explanation / Answer

When light passes through first polarizer, it's intensity will be reduced to half

I1 = I0*(cos A1)^2

After that when light passes thorugh 2nd polarizer, Intensity will be

I2 = I1*(cos A2)^2

After that when light passes thorugh 3rd polarizer, Intensity will be

I3 = I2*(cos A3)^2

I3 = I1*(cos A2)^2*(cos A3)^2

I3 = I0*(cos A1)^2*(cos A2)^2*(cos A3)^2

Now using given values:

I0 = Ii = 14

A1 = 17 deg

A2 = theta2 - theta1 = 44 - 17 = 27 deg

A3 = theta3 - theta2 = 58 - 44 = 14 deg

So

I3 = 14*(cos 17 deg)^2*(cos 27 deg)^2*(cos 14 deg)^2

I3 = If = 9.57 units

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