# Making density disturbance visible with Moiré stripes

### Basic principle

If you put two similar striped patterns together, Moiré stripes result. If the patterns are identical, Moiré stripes don't occur, but if the patterns are just slightly different, interference fringes based on that gap occur.

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 The refractive index of salt water is dependent on its concentration. As the concentration increases, the refractive index also becomes larger. Therefore, a light source shone horizontally into a stratified fluid will refract in the direction of the concentration gradient. Using these characteristics, by looking at a striped interference fringe through a stratified fluid will make the density disturbance in that fluid visible.

### A stratified fluid body in a square water tank

First you paint a vertical striped pattern (G1) on a light box, and then print a striped pattern with a thinner pitch (G2) on an acrylic sheet, and place it a small distance from the light box. Normally if you look through the acrylic sheet at the light box, Moiré stripes become visible, but if you look from a certain distance, the two striped patterns match completely, and the Moiré stripes disappear.

Having established this distance, place the water tank in front of the acrylic sheet (G2) (placing it behind the sheet is also OK) and make a stratified fluid in the tank.

Light passing through the stratified layers is refracted downwards, however since the striped pattern is vertical, the matching of the two striped patterns doesn't change. When waves occur in the stratified fluid, the light is refracted horizontally, and the striped pattern on the light box is distorted to make Moiré stripes. These Moiré stripes are isopleths (equal value lines) of the horizontal density gradient, so if the amplitude and direction of the waves is constant, the stripes are also lines denoting equal phase.

The sensitivity of this technique increases as you move the two striped patterns apart and decrease their pitch. However, in order to photograph the Moiré stripes, both striped patterns must be in focus, so you cannot infinitely raise the sensitivity.

### A stratified fluid in a cylindrical water tank

When the walls of the water tank are curved, even when the fluid is at rest, the refraction of light through the water tank is inconsistent. Therefore it is almost impossible to completely eliminate the Moiré stripes. Even so, if you photograph one of the striped patterns twice at points where the phase of a wave is 180 degrees different, and combine the photos after, clear Moiré stripes can be obtained.

The most important thing about this technique is to combine the two striped patterns with more precision than their pitch. Combining two different frames on the same roll of film accurately is extremely difficult. One way of getting around this is to make the laboratory dark, leave the camera shutter open for a half-period of the wave, and flash two strobes once each, again a half-period apart, thereby creating two images on the one frame. I f you use color film, and change the color of the strobes by covering them with red and blue film respectively, you can split the two images using computer processing and thereby create Moiré stripes.