# Exploring the Law of Malus: Understanding the Intensity of Polarized Light

• icebox105
In summary, the law of Malus states that the intensity of unpolarized light is reduced by half when it passes through a polarizer.
icebox105
This is more of a conceptual question:

Where does the equation for the intensity of polarized light come from?

I know the standard form is:

I=(1/2)(I_0)

after the EM wave passes through the first polarizer. Why is that? Why is the intensity exactly half?

The polarizer ensures that the only polarizations of light that pass through are those oriented along the same axis as the polarizer. Since the polarization of the light is random, this means any number of the polarizations could be eliminated, right? I am having difficulty understanding how a polarizer automatically blocks out 50% of the light at all times, and how this is true regardless of the angle of the polarizer, since the polarizations are random to begin with.

Are you familiar with the law of Malus?

If you think of the light as an electromagnetic wave, the orientation of its E field represents its polarization angle. The nature of an ordinary dichroic polarizer is to strongly absorb the E field in one direction, allowing the field perpendicular to that direction to pass through. The light that makes it through the polarizing "filter" has its field realigned with the polarization of the filter. Ignoring loss, if polarized light ($E_0$) passes through a dichroic filter at an angle $\theta$, the transmitted beam is now polarized parallel to the orientation of the filter's axis and has a field strength of $E_0 \cos\theta$. The intensity of the beam is reduced to $I_0\cos^2\theta$--the law of Malus.

Now if the incoming light is unpolarized, you can think of its polarization as being randomly distributed over all angles. The average of $\cos^2\theta$ is 1/2. So the intensity of the transmitted light is $I = I_0/2$.

Make sense?

Yes! Thank you for the explanation, especially the last bit. We covered the Law of Malus in my class, but didn't refer to it by that title. I think the thing I was really missing was the fact that the average of cos(sq) is 0.5, which makes complete sense if I graph it and think about it.

Thanks again!

## What is polarization of light?

Polarization of light refers to the orientation of the electric field vector of a light wave. When light is polarized, the electric field oscillates in a specific direction as the wave propagates, rather than in all directions like unpolarized light does.

## How does light become polarized?

Light can become polarized through various processes such as reflection, scattering, and transmission through polarizing filters. These processes can selectively filter out certain orientations of the electric field, resulting in polarized light.

## What are the types of polarization?

The two main types of polarization are linear polarization, where the electric field oscillates in a single plane, and circular polarization, where the electric field rotates in a circular motion. There is also elliptical polarization, which is a combination of both linear and circular polarization.

## Why is polarization important?

Polarization is important in various applications such as photography, 3D movies, and LCD screens. It also plays a crucial role in understanding the nature of light and its behavior in different mediums.

## Can all types of light be polarized?

No, not all types of light can be polarized. Only light waves with transverse electromagnetic fields, such as visible light, can be polarized. Longitudinal waves, such as sound waves, do not have an oscillating electric field and therefore cannot be polarized.

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