# Light through polarizing filters

Since a long time I am intrigued by the following experiment: Polarizing filters remove light polarized at 90° to the filter's polarization axis. If a horizontal polarizer is placed on top of a vertical polarizer, there is minimal light transmission. So far "understandable". Now put a third polarizing filter in between the other two filters at an angle of 45 degrees (diagonally) and light gets through! is there anyone that can at least try to make this understandable for me?

Meir Achuz
Homework Helper
Gold Member
At some point you have to believe the mathematics (of Malus' law in this case)
and not look for a more naive explanation.

or Murphy's Law

Since a long time I am intrigued by the following experiment: Polarizing filters remove light polarized at 90° to the filter's polarization axis. If a horizontal polarizer is placed on top of a vertical polarizer, there is minimal light transmission. So far "understandable". Now put a third polarizing filter in between the other two filters at an angle of 45 degrees (diagonally) and light gets through! is there anyone that can at least try to make this understandable for me?
Imagine to swing on a vertical axis a rope held on a wall at one end: you move up and down the other end and you make the rope take the form of a vertically polarized wave. Then put, half distance from your hand and the wall, a big disk with a diametrical slit so that the rope goes through it, and rotate the disk at various angles; the wave can pass perfectly through the slit when this is vertical, it doesn't pass through it when it is horizontal, and it have a reduced amplitude in the other cases; specifically, it will (theoretically) have half amplitude at 45°, and it will be 45° polarized in this case (can you see it? Think about components).

If now you put another disk, further rotated of 45° (so that it is at 90° with respect to the vertical, that is, horizontal), then half of the last wave will pass, so you have now 1/4 of the initial amplitude.

So, a single horizontal disk (at 90°) will block the wave completely, while two disks at 45° the first and 90° the second will transmit 25% of it.

Last edited:
Meir Achuz
Homework Helper
Gold Member
I think Malus is simpler.

So cruel; lightarrow gave an excellent explanation that reminds us why this is purely a classical wave phenomenon.

The incident sinusoidal light wave passes readily through a parallel polarizer. When a second polarizer is oriented perpendicular to the first, the projection of the light wave through the second polarizer has an output amplitude of zero, i.e., cos290o=0

In the case with an intervening 45o offset polarizer, the projection of the incident wave through the intermediate polarizer reduces the initial amplitude by a factor cos245o=1/2. The transition through the third polarizer has a similar projection, where now the initial amplitude is reduced by an overall factor 1/2 x 1/2=1/4.

So cruel; lightarrow gave an excellent explanation that reminds us why this is purely a classical wave phenomenon.
Thanks! Imagine to swing on a vertical axis a rope held on a wall at one end: you move up and down the other end and you make the rope take the form of a vertically polarized wave. Then put, half distance from your hand and the wall, a big disk with a diametrical slit so that the rope goes through it, and rotate the disk at various angles; the wave can pass perfectly through the slit when this is vertical, it doesn't pass through it when it is horizontal, and it have a reduced amplitude in the other cases; specifically, it will (theoretically) have half amplitude at 45°, and it will be 45° polarized in this case (can you see it? Think about components).

If now you put another disk, further rotated of 45° (so that it is at 90° with respect to the vertical, that is, horizontal), then half of the last wave will pass, so you have now 1/4 of the initial amplitude.

So, a single horizontal disk (at 90°) will block the wave completely, while two disks at 45° the first and 90° the second will transmit 25% of it.
Interesting explanation. But the rope can't move vertically before the 45 degree slit and diagonally behind it ! Instead the rope would move a little sideways even before the slit. Does this happen with the EM wave too ? Not sure.

I guess the trouble with the polarizer comes from the easily overseen fact, that it is a nonlinear element (as in the rope case if this explanation is correct). Which one can see from the fact that the light path is not reversible. Send a vertically polarized beam to the 45 degree filter and it comes out at 45 degrees. But sending a 45 degree beam from behind doesn't give you a vertically polarized one.