Category: 09 Waves


A mechanical model of polarization.

Explanation of Malu’s Law

Demonstration of Polarization of Light

explanation at xmdemo

Applet animation of polarisation of EM waves.

🍏 Polarizers {cabrillo applet}

Even though most natural light sources are unpolarized light, it is not difficult to find polarized light around us if you know where to look.

explanation at xmdemo

LCD projectors are my favorite sources of polarized light.

explanation at xmdemo

Check out my Einstein-Newton demonstration. Some 3D movies are made based on the same principle.

explanation at xmdemo

Also, light actually become partially polarized after reflection off water, glass, etc. (This is why we put on polarizing sunglasses.)

explanation at xmdemo

Phase Relationship

We can apply the concept of phase to any repetitive periodic motion. One complete cycle corresponds to 360° or 2π rad. Half-a-cycle corresponds to 180° or π rad. A quarter-cycle coreesponds to 90° or π/2 rad. So on and forth.

These four oscillations are in-phase with one another (phase difference of 0, 2π, 4 π, …)

The 1st and the 3rd are complete out-of-phase (phase difference of π, 3π, 5 π, …) with the 2nd and the 4th.

Each oscillation lags the one on the left a quarter-cycle (π/2 rad).

Each oscillation lags the one on the left by 1/8 of a cycle (45° or π/4 rad).

The profiles of two progressive waves moving from left to right are now clearly visible. There is the transverse wave in the bobbing heads, and the longitudinal wave in the gyrating hips. 😛

In an actual progressive wave, there is a continuous increasing phase lag in the direction of wave propagation. Each wave element lags the preceding wave element by a bit.

Wave Speed

Notice that a wave crest always advances by one wavelength after every one period? That’s why v=λ/T, or v=fλ.


For the same medium, wave speed is constant. So when frequency goes up, wavelength does down. In the animation below, both waves have the same speed. So doubling the frequency always result in halving of wavelength.


In different medium, the wave speed is different. When a wave crosses from one medium to another, the frequency does not change, but the speed and wavelength do. In the animation below, both waves have the same frequency. The one with the longer wavelength propagates at a faster speed.

For the original 🍏, click <here>

Nothing can out run a light wave. But for other waves, it is possible for the medium to travel faster than the wave. When this happens for water waves, we get the wake. When this happens for sound, we get the sonic boom. When it happens for the slinky, we get a hovering monkey. Watch this video for a dramatic demonstration.

explanation at xmdemo