# Q & A: Light transmission through three polarizers

Most recent answer: 08/20/2013
Q:
is this the best explanation? http://answers.yahoo.com/question/index?qid=20090116053436AA8P1Ct
- Dylan (age 17)
NY, USA
A:
For those who don't want to bother with the link, the question was this. Two polarizers rotated 90° from each other don't transmit light. Yet inserting a third in between at 45° from each allows some light to pass. Why?

The answer you cite is ok, although it gives a somewhat false picture of how polarizers work at a microscopic level. I'll try to do better, and shorter.

Let's delay discussing how polarizers work. The point is that they block all light whose electric fields are along some direction, say vertical, while allowing most light with electric fields at right angles to that to pass. So if the first polarizer lets horizontally polarized light (call it 0°) through and the second only lets vertically polarized light (90°) through, nothing gets through.

What happens when you insert that 45° polarizer in between? The key point is that the horizontal fields that hit it can be expressed as the sum of 45° fields (transmitted) and 135° fields (blocked). That's the same as how you can express a move northeast as a sum of a north move and an east move. The 45° fields that hit the 90° (vertical) polarizer can be expressed as the sum of 90° fields (transmitted) and 0° fields (blocked).

Now let's ask how a polarizer can work. It's easiest to see for long-wavelength radiation, say microwave, whose interaction with matter can sometimes be treated classically, rather than for the quantum interactions of visible light and matter. Take a grid of lots of closely spaced horizontal wires, not quite touching. They can carry electric currents horizontally but not vertically. A vertical microwave field will pass right through the grid. A horizontal one will drive currents in the wires, which heat them up, pulling energy out of the wave. With a few layers of these wires, the horizontal wave is blocked. For visible light the picture isn't right but in effect the orientation of the transition dipoles accomplishes the same thing.

Mike W.

(published on 02/07/2011)

## Follow-Up #1: polarizer magic

Q:
I was reading a book on physics that says if you align two polarizers in such a way as to prevent any light coming through, you can add a third polarizer between the two original polarizers and your eye and by turning the third polarizer, you again see the light..This seem inexplicable.. but the book insists its true...Is it? and if so why? Thanks
- Charlie (age 69)
Johnston, RI
A:

It's true, and easy to check. Polarizers are cheap. (I assume you mean the one you turn is between the other two. If you put it betwen your eye and the others, it won't work.)

See this thread for one explanation of how it works.

Mike W.

(published on 08/18/2013)

## Follow-Up #2: three polarizers

Q:
Mike I see that somehow I made a mistake in asking the question..I was told that inserting a third polarizer "after" the other two would result in light passing through even though it had been blocked by the first two,,change "between" to "after" This is in a physics book that is referring to strange properties of polarized light..
- Charlie (age 69)
Johnston, RI
A:

You're right. Once the light has been blocked, the next polarizer won't unblock it. Only inserting it in between works.

Mike W.

(published on 08/19/2013)

## Follow-Up #3: captcha code

Q:
Thanks Mike...So the physics book at the library is wrong.. and fyi this code thing is a real pain,,,entered the code a half dozen times and still gets refused.
- Charlie (age 69)
Johnston, RI
A:

Sorry about that captcha code. Before it was installed it had become almost impossible to use the system because of the huge number of fake questions, mostly ads,  submitted by bots. There is, after all, a limit to how much viagra a volunteer team can buy.

Mike W.

(published on 08/20/2013)