Visualizing Polarization

Classically, light is an electromagnetic wave– a wave of oscillating Electric and Magnetic fields instead of oscillating molecules of air or water like in sound or water waves. Electric and Magnetic fields are not something we can “see”, but when they oscillate in synchrony, it results in a visual phenomenon called light!

Light, a universal phenomenon that has existed since the universe began, responsible for the beautiful night sky and your existence, can be described by just four equations, collectively called the Maxwell equations:

(1)   \begin{align*} \vec{\nabla}\cdot\vec{E}=&0\\ \vec{\nabla}\times\vec{E}=&-\dfrac{\partial \vec{B}}{\partial t}\\ \vec{\nabla}\cdot\vec{B}=&0\\ \vec{\nabla}\times\vec{B}=\dfrac{1}{c^2}\dfrac{\partial \vec{E}}{\partial t}\\ \end{align*}

The above equations are “sourceless” Maxwell equations in Vacuum — whatever that means. The vectors \vec{E} and \vec{B} denote the variables: Electric and Magnetic fields. Rearranging to separate the equations in \vec{E} and \vec{B}, we get the very familiar wave equations in \vec{E} and \vec{B} that are identical to the wave equations in mechanical waves, say, on a guitar string! The solutions to the wave equations are oscillating Electric and Magnetic fields.

One example of a solution is

(2)   \begin{align*} \vec{E}=&E_0\cos(kx-\omega t)\hat{y}\\ \vec{B}=&B_0\cos(kx-\omega t)\hat{z}\\ \end{align*}

In Eqns. (2), E_0, B_0 are amplitudes of the Electric and Magnetic fields. The oscillation comes from the \cos(kx-\omega t) terms, and the direction of oscillation is given by the unit vectors \hat{y} and \hat{z}. (Try substituting the solutions in (2) back into the Maxwell equations in (1) and verifying that they solve them.)

When we say light is linearly polarized, we mean that the Electric field (\vec{E}) oscillates in one fixed direction all throughout space. For instance, the light due to (2) is linearly polarized in y direction.

Light coming from natural sources is generally unpolarized and can’t be written in the form of (2). But one can use polarizers, materials that allow Electric fields to oscillate only in one direction, to polarize light and make the math easy.

Oscillating vectors and their polarization may not be the easiest things to visualize, so we present a simple demonstration using a mechanical wave on a rope.

Click the buttons below to view the demonstrations set up by Pavan:

Set up: We created circular waves on the rope by hand at one end while keeping the other end pivoted. The amplitude and direction of the oscillation of each point on the rope is analogous to the Electric field’s magnitude and direction. These oscillations of the string form a wave that propagates along the string, which is analogous to the direction of light propagation. Clearly, the oscillations are not restricted to one direction. We then introduce a slit using two rulers which acts as a polarizer, allowing a wave of oscillations only in one direction (along the slit) to pass.

In Demo 1, we put the rulers vertically. So when a circular wave passes through it, the resulting wave oscillates vertically while the horizontal oscillations vanish. In Demo 2, we add a horizontal slit, which cancels the vertical oscillation too. So we end up having no oscillation at all; that is, no light passes through two linear polarizers placed perpendicular to each other.

What would happen when we pass light through two polarizers that are at, say, 60 degrees angle to each other?

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Acknowledgements

Murthy initiated the idea of demonstrating polarization of light using this simple set up. We also thank Murthy for his inputs to improve the post. Pavan set up the demo.

Credits

Video credits: Pavan Konkipudi, Research Assistant in Physics, Azim Premji University

Suggested reading

Griffiths, David J. (David Jeffery), 1942-. Introduction to Electrodynamics. Boston :Pearson, 2013

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