Refractive Index Techniques 1: Liquid Surfaces

Figure 1: A beam is reflected and refracted at a sudden change in refractive index. Jean Biz Hertzberg 2023 CC-BY 4.0 via Wikimedia Commons.

As we saw in the Overview Choice 2, if a light ray suddenly encounters a fluid or medium with a different index of refraction, two things happen. 1) The light bends towards or into the fluid with the higher index of refraction, according to Snell’s law. This bending is what we call refraction. Let’s consider it a type of transmission of light through the medium.  2) The other thing that happens when light hits a sudden change in refractive index is reflection. Figure 1 shows a beam of light being transmitted through air before hitting a semi-circular glass lens. The amount reflected depends on several factors, which we’ll discuss later on.

Why does refraction happen? It’s because a transparent medium slows light down. This turns out to be related to the wave nature of light, and how light’s electromagnetic (EM) waves interact in a fairly subtle way with electrons’ EM waves in the medium . Figure 2 shows how the drop in speed and the constant frequency  (see Photons, Wavelength and Color) shortens the wavelength and shifts the direction.

Figure 2: A plane wave changing direction, wavelength, and speed when the refractive index increases. By Jacopo Bertolotti, CC0, via Wikimedia Commons

There are a number of flow vis techniques based on refraction. Firstly, we’ll see what happens at free gas-liquid interfaces, then we’ll consider thin-film effects. Lastly, we’ll cover shadowgraphy and schlieren in a bit of depth. Along the way we’ll see a variety of fluid physics being illustrated as well.

Gas-Liquid Interfaces

One of the most common and fascinating flow visualizations occurs where air and water meet. Nearly every human on the planet has played with splashing a hand in water and watched droplets fall in a pool. Water and air are both transparent; we can see the interface only because the index of refraction of water is so much higher than in air. Flat water will act as a mirror, with the amount of light reflected depending on polarization and angle of incidence (measured from the perpendicular to the surface) as shown in Figure 3.

Figure 3: Water reflectivity increases with angle of incidence. By Dan Pangburn, CC 3.0 via Wikipedia

This is used to good effect in Figure 4, where the color of the pool is set by the background.

Figure 4: Light reflects from standing waves on the surface of water in an ultrasonic cleaner. Daniel Lopez, Get Wet 2013.

Figure 5: Refraction through a non-flat surface creates regions of high intensity, where many rays cross, known as caustics. Jacopo Bertolotti, CC0, via Wikimedia Commons


In addition to reflection, refraction happens when light passes from air into water. As shown in Figure 5, an irregular water surface takes uniform parallel light and concentrates it into brighter and darker areas, called caustics . Note that Figure 5 illustrates the case of light emerging from the water into air. If you’ve spent time relaxing near a body of clear water, you may enjoy pleasant associations from the more familiar case of sunlight entering water shown in Figure 6.

Figure 6: Sunlight is concentrated into caustics by small waves on the water surface, here near a Caribbean beach. Ryan Lumley, Team Second Spring 2014.


Figure 7: A rectangular tank, partially filled with water, was tipped on edge. Sunlight projected through the waters’ edge to the ground. Ripples on the water surface concentrated the sunlight into caustics, and the thin film at the water’s edge dispersed the sunlight into component colors. Owen Hnath, Gordon Browning, Tracy Eliasson, Travis Gaskill, Trisha Harrison, 2007, Team Second assignment.

Figure 7 shows another example of caustics, plus other optical and fluid physics. This image was generated with an easy but unusual setup, as shown in Figure 8: a transparent tank of water tipped at an angle in sunshine, with the image photographed on the ground beneath the tank. As water sloshed in the tank, wetting and de-wetting contact lines were alternately formed at the air-water-tank (three phases of matter!) interface. Contact lines are an active area of study, particularly interesting to applied mathematicians since early models included a mathematical singularity . In this case, the de-wetting contact line formed a small prism, creating a faint rainbow along the image of the water’s edge. This demonstrates that water is an optically dispersive medium, meaning that the refractive index of water varies at least slightly with the wavelength of light. The result is a rainbow: sunlight is dispersed into the different wavelengths (colors) of light since they are refracted at different angles. The strong diagonal and simplicity of the image are an added bonus.

Figure 8. Apparatus of Figure 7. JeanBizHertzberg 2023.

Thin Film Effects

Thin film interference also depends on the combination of reflection and refraction at sudden changes in refractive index . This is the effect that gives soap bubbles, oil slicks, and certain birds and butterflies their colors.

Figure 9: A wave of light reflecting off the upper and lower boundaries of a thin film. Nicoguaro, CC BY 4.0, via Wikimedia Commons

The thin film effect requires that the thickness of the film be no more than a micron in thickness. Figure 9 shows that the refracted beam has a longer distance to travel than the reflected beam. If this additional distance is equal to a multiple of the wavelength, then the two beams  will be in phase and will add together. This is constructive interference . This only works for a particular wavelength for a given incident angle, film thickness, and refractive index. That combination acts like a combined filter and amplifier, so only one wavelength — one color — emerges stronger. The waves for other colors won’t add, and will instead cancel (to some degree). As the layer thickness varies, so will the amplified color. The resulting rainbow of colors, thus, indicates the layer thickness with great sensitivity.This is illustrated in Figure 10, where sugar grains in the soap film cause minute changes in thickness.

FIgure 10: A horizontal soap bubble film drains towards its center, while nonuniformities from undissolved sugar crystals create colored patterns as the film thickness varies. Dennis Can, Alisen Bol, Fiona Wohlfarth, Team First 2015.

If the thickness is too large, small differences between portions of the incoming beam will wash out the effect, and the colors will fade. At the other end, if the thickness is too thin, such that no (visible) wavelength can interfere constructively, then the surface will be transparent. This phenomenon is accompanied by an instability in the film called ‘critical fall’ , which creates small islands of thicker film as shown in Figure 11.

Figure 11: In a draining soap film, an instability develops between the extremely thin black soap film area and the slightly thicker silver area below, just before the film breaks. Nicholas Travers, Ryan Kelly, Andrew Fish, Doug Schwichtenberg, George Seese. Team First Spring 2012.



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Dye Techniques 3 – Light Emitting Fluids
Refractive Index Techniques 2: Shadowgraphy and Schlieren