# Q & A: Light waves through polarized sunglasses

Q:
What happens when light waves go through two consecutive polarized sun glasses? . . . Given the first pair of polarized sunglasses would knock out most of the horizontal waves, are the continued waves all vertical? of rather do the waves resume vibrations in two perpendicular directions? I understand that "all" light waves pulse two ways in 3-D space,say vertical, then horizontal for simplicity.
- Ron Bauman (age 67)
Flagstaff AZ USA
A:
Hello Ron,

Let's assume that polarized sunglasses act as perfect polarizers, meaning that the light waves that have passed through the lenses have only one specified polarization.

After passing through the first pair of polarized lenses, and assuming that the lenses are vertically polarized (which is usually the case for sunglasses), the horizontally polarized waves would then be absorbed by the polarized lens. Thus, the light waves that have passed through them would be only vertically polarized and they would stay vertically polarized.

If these vertically polarized waves are then passed through another pair of lenses, the final polarization would be the same as the polarization of the second pair of lenses.

An interesting thing to take note of is that the intensity of the resultant light as compared to the intensity incoming light would follow the following formula known as Malus's law.
I = I0 ( cos(θ) )2
where
I is the intensity of the incoming light
I0 is the intensity of the resultant light
θ is the angle between the polarization of the incoming light and the polarization of the polarizing lens.

This means that if vertically polarized light hits a polarizer that has horizontal polarization, the intensity of the resultant light will be zero!
You could see this effect by placing two polarized sunglasses lenses together (one in front of the other). Then, while looking through the both of them, rotate either lens by 90 degrees to "dim" the image you're looking at.

I have included a simple diagram below to illustrate the above-mentioned concepts to you. Maurice

(published on 03/27/2012)