Understanding Wave Polarisation: Intensity Changes and Filter Effects Explained

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question dude
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I have two queries:

- if unpolarised light passes through a polaroid filter so that light coming out of the filter becomes polarised, would intensity (brightness) of the light become reduced as a result?

- if you have a polarized wave, and it passes through a filter that has a gap which is at an angle to the plane of this polarized wave's vibrations (but not perpendicular to it), would anything come out of the filter? (just to give an example, say you have a wave vibrating up and down in the vertical plane, I understand that if you have a filter which only has horizontal gaps then nothing will come out of the filter, but what if the gap was at an angle somewhere between vertical and horizontal?)


if I haven't made myself clear, please tell me, I can get hold of the textbook and scan the diagram
 
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question dude said:
I have two queries:

- if unpolarised light passes through a polaroid filter so that light coming out of the filter becomes polarised, would intensity (brightness) of the light become reduced as a result?

Yes, the intensity will be reduced.
- if you have a polarized wave, and it passes through a filter that has a gap which is at an angle to the plane of this polarized wave's vibrations (but not perpendicular to it), would anything come out of the filter? (just to give an example, say you have a wave vibrating up and down in the vertical plane, I understand that if you have a filter which only has horizontal gaps then nothing will come out of the filter, but what if the gap was at an angle somewhere between vertical and horizontal?)

The intensity of the light can be found by the following equation.
I=I0cos2θi
Where I0 is the initial intensity of the light before passing through the polarizer and θi is the angle between the light's initial polarization direction and the axis of the polarizer.
 
Drakkith said:
Yes, the intensity will be reduced.The intensity of the light can be found by the following equation.
I=I0cos2θi
Where I0 is the initial intensity of the light before passing through the polarizer and θi is the angle between the light's initial polarization direction and the axis of the polarizer.

thank you very much, although I'm not up to that standard yet so I haven't come across it (I'm in high school here), the formula there makes sense, because cos 0 = 1, so the intensity would be exactly the same if the gap is in the exact plane as the wave's vibration, and cos 90 = 0 if the gap is right angle to the plane in which the wave vibrates in