Polarizing filter not extinguish the wave although 90 degree polarizers

[Felipe Lincoln]

When a non-polarized electromagnetic wave cross a polarizer filter, its intensity drops to a half. Then this now polarized wave cross a polarizer such that it has 90 degree compared to the other. The wave is completely vanished. But if we put another polarizer with, let's say 45 degree in comparison with the first, the wave pass through all the three polarized and is not vanished. Its intensity is $\frac{1}{2}I_0\cos^245\cos^245$.
It seems that the tricky happened when the polarized wave let's with 0 degree from the vertical axis passes through the 45 degree polarizer it breaks into vertical and horizontal components, if it wasn't true the wave would disapear when crossing the last 90 degree polarizer (horizontal).
Why the wave doesn't disapear after adding the third polarizer in between the two perpendicular polarizers?

 

[Nugatory]

This is a quantum mechanical phenomenon, and it's one of the neater demonstrations of how quantum mechanics is different from classical mechanics (it might be the only one that is routinely done in high-school labs).

The tricky thing you're looking for is that a polarizing filter does more than just absorbing some of the light; whatever passes the polarizer is also polarized in the direction of the filter. The light that leaves the first polarizer is vertically polarized, and none of it can pass through the horizontal filter ($cos^2(90)$ is zero). But if it encounters a 45-degree polarizer on the way, half of it passes through ($cos^2(45)$ is 1/2) and that surviving half is now polarized at 45 degrees. When this encounters the horizontal filter, the angle with the horizontal is 45 degrees, so half of it passes through.

 

[sophiecentaur]

I would have thought that the OP is correct and that there is no need for the doubt that's written in the final paragraph as it's already been explained fine in classical terms. The OP doesn't mention photons.

This is a quantum mechanical phenomenon, and it's one of the neater demonstrations of how quantum mechanics is different from classical mechanics (it might be the only one that is routinely done in high-school labs).

Maybe that comment applies to some kinds of polariser but the same effect can be observed using a very classical wire grid and plane polarised microwaves. As far as I know, the way such a polariser works is explained using Maxwell's Equations. The wire polariser passes components of one polarisation and reflects the other components.
I agree that the quantum level explanation is somewhat harder to take on board but, as with many phenomena, one of the two approaches is often more convenient than the other. Interference and diffraction (both taught at a similar level in School) can also be approached from either direction but surprisingly (?) the resulting mathematical expressions are the the same.

 

[Mentz114]

[]
Maybe that comment applies to some kinds of polariser but the same effect can be observed using a very classical wire grid and plane polarised microwaves. As far as I know, the way such a polariser works is explained using Maxwell's Equations. The wire polariser passes components of one polarisation and reflects the other components.
I agree that the quantum level explanation is somewhat harder to take on board but, as with many phenomena, one of the two approaches is often more convenient than the other. Interference and diffraction (both taught at a similar level in School) can also be approached from either direction but surprisingly (?) the resulting mathematical expressions are the the same.

That is interesting. I found this^* which looks meaty.

*
http://www.hep.princeton.edu/~mcdonald/examples/polarizer.pdf

 

[sophiecentaur]

It certainly is 'meaty' for one as out of touch as I am. The result of all that seems to agree with the notion that the transmitted wave is more or less linearly polarised normal to the wires. It's a pretty easy A level experiment to perform with basic microwave equipment and you get the 'right' answer.

 

[sophiecentaur]

. . . . . . the phenomenon of polarisation rotation occurs all over the place in the RF world. Broadcasters go to a lot of trouble to arrange for nearby co-channel transmitters (all frequencies) to use orthogonal polarisations in order to help receiving antennae to select the wanted signal and reject the unwanted. Problem is that nearby metal structures (diagonal) can re-radiate components of the 'cross' polar wave and spoil the selectivity that's been aimed at.

 

[vanhees71]

This is a quantum mechanical phenomenon, and it's one of the neater demonstrations of how quantum mechanics is different from classical mechanics (it might be the only one that is routinely done in high-school labs).

It's also perfectly valid within classical electrodynamics. It's of course true that it is valid in QED as well.