Changing polarization of light
We want to rotate the direction of polarization of a beam of polarized light through 90 degrees by sending the beam through one or more polarizing sheets. What is the minimum number of sheets required if the transmitted intensity is to be more than 60% of the original intensity?
Why does the number of sheets used change the drop in intensity? I thought that was completely based on the angle changed.
Answer
When a polarized beam travels through a polarizing sheet, its new intensity is
I = I_0 * cos^2(Δθ)
where Δθ is the difference in angle between the beam's polarization and the sheet's polarization. As you can see, the intensity will always be reduced. Obviously we want the total angle change to be 90 degrees, but we can achieve this in smaller increments of Δθ. After applying n sheets, the reduction will be
I / I_0 = cos(Δθ)^2n
and nΔθ = 90 degrees. Solve for the number of sheets n that gives you an intensity of 60% the original.
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When a polarized beam travels through a polarizing sheet, its new intensity is
I = I_0 * cos^2(Δθ)
where Δθ is the difference in angle between the beam's polarization and the sheet's polarization. As you can see, the intensity will always be reduced. Obviously we want the total angle change to be 90 degrees, but we can achieve this in smaller increments of Δθ. After applying n sheets, the reduction will be
I / I_0 = cos(Δθ)^2n
and nΔθ = 90 degrees. Solve for the number of sheets n that gives you an intensity of 60% the original.