Polarizing unpolarized light

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In summary, when passing through a polarizing filter, the intensity of unpolarized light is reduced by 50% due to Malus' law, which states that the intensity varies as the square of the cosine of the angle. However, for an unpolarized initial beam, there are many random linear polarization directions and therefore the average cos^2 value is 1/2, resulting in a 50% reduction in intensity.
  • #1
jdstokes
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Why does a polarizing filter transmit 50% the intensity of unpolarized light?

I would have thought that since only 0.5 of the electric field gets through, this would cut down the intensity by 0.5^2 = 0.25?
 
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  • #2
It may be easiest to think in terms of energy. If half the energy is in the horizontal polarization and half in the vertical, whhen I remove half, half is left.
 
  • #3
jdstokes said:
I would have thought that since only 0.5 of the electric field gets through, this would cut down the intensity by 0.5^2 = 0.25?

Well, not half of the E-field gets through. If you take a random orientation (uniformly distributed) between 0 and 90 degrees (noted by angle A) then the component that gets through is cos(A). We have to average cos(A) between 0 and 90 degrees then (or, in radians):

2/pi x integral(cos(A) dA between 0 and pi/2) = 2/pi.
 
  • #4
jdstokes said:
Why does a polarizing filter transmit 50% the intensity of unpolarized light?

I would have thought that since only 0.5 of the electric field gets through, this would cut down the intensity by 0.5^2 = 0.25?

That's a great question;
the answer lies in Malus' law which states that the intensity of the transmitted light thru a polarizer varies as the square of the cosine of the angle...

I = I*[cos^2 (X)]

However, that is not the whole story. For an Unpolarized initial beam there are many linear polarization directions which are randomly oriented and so they have an average cos^2 value of 1/2.

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  • #5
Thanks all for your replies. I found a neat explanation that goes like this. Assume that the initial light is equally polarized in N random directions [itex]\theta_i[/itex]. Then the intensity transmitted according to Malus' law is

[itex]I = \frac{I_0}{N}\cos^2\theta_1 + \cdots = I_0 \frac{1}{N}\sum_{i=1}^N \cos^2 \theta_i[/itex], which is just the average of cos^2 as N tends to infinity (i.e., 1/2).
 

What is polarized light?

Polarized light is a type of light that has its electric field oscillating in a single plane. This means that the light waves are all oriented in the same direction.

What is unpolarized light?

Unpolarized light is a type of light that has its electric field oscillating in multiple planes. This means that the light waves are oriented in different directions and are not aligned.

How is polarized light created?

Polarized light can be created by passing unpolarized light through a polarizing filter. This filter only allows light waves oscillating in a specific plane to pass through, resulting in polarized light.

Why is polarized light important?

Polarized light is important in various scientific and technological applications. It can be used for glare reduction in sunglasses, 3D movie technology, and in studying the properties of light in materials.

Can polarized light be unpolarized?

Yes, polarized light can be converted back to unpolarized light by passing it through a second polarizing filter at a 90 degree angle to the first one. This process is known as depolarization.

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