Of Evening Sun and Blue Milk

When I was a child, I often wonder why the sky appear blue. All these while I didn't get a precise answer from people that I've asked because the mechanism that was responsible in making the sky blue require some understanding of optical physics to explain it.

PHYSICS SIMPLIFIED

Truth be told, concepts involved in classical physics are rather simple most of the time, and yet the effects coming from such simplistic theories are often profound. Physical theories that are expressed in mathematical equations quantitatively explain physical phenomena. Therefore, as the language of physics, mathematics always brings connection between parameters involved in a certain phenomena.

Even though mathematics has this capability to express how nature behaves in symbols, it is meaningless if it is not interpreted correctly. That is why physicists and educators who are passionate in education of physics always desire to simplify complicated equations into components and express it in terms of language, which most of us could understand.

INTRODUCTION

What I have today, is a demonstration of a physical phenomena that is so ubiquitous to us that we usually take it for granted. We often (probably from the curiosity of a child) asked this question ever since we can remember, but as time and growth progress, most of us care too little to seek an answer to it. Nevertheless, I believe somewhere in the inner-child, the search is always on.

The objective of this demonstration is to show the principal phenomena of light scattering, a mechanism that is responsible for making the daylight sky, blue. I demonstrated this using L.E.D light scattered by a milk-water dilution. They are essentially the same phenomena being brought in a smaller, experimentally viable scale.

THE CONCEPT OF SCATTERING

Scattering in essence is the removal of energy from an incident wave, in our case, light-waves, by a scattering medium (milk-water dilution) and the re-emission of that "loss" of energy in many other directions, which we will see as the result of our demonstration.

This kind of scattering (Rayleigh Scattering) is predominant when the scattering particles are smaller than the length of each light-wave cycle (wavelength). In our case, tiny milk particles are actually little globules of fat suspended in water. When it is diluted thin enough such that light can pass through it, the fat-molecules become our scattering medium.

[detail explanation of Rayleigh scattering is available at the footnote of this article.]

When light shines on these tiny bits of fat (they are actually colloidal particles), the electrons in it absorbs the energy, starts to oscillate, and re-radiate the energy in the form of light in another frequency (a different colour). Following the law of Rayleigh scattering which states the power of radiated energy is directly proportional to the fourth power of the frequency of the incoming light:  

P ∝ (2πf)^4

It shows the tiny oscillating particles radiate more energy in higher frequency compared to lower frequency. What this implies, is that blue coloured light, having higher frequency gets scattered away more compared to red coloured light, which has a lower frequency. In fact, calculations shows the scattered power for violet light (wavelength: 400 nm) is about 10 times stronger than red light (wavelength: 700 nm) [note: wavelength is inversely proportional to the frequency]

This is the reason why diluted milk will appear blue when it is shined by a white light. [refer to the cover photo of this blog post. The thinning filaments of milk diffusing in clear water appears blue]

METHODOLOGY & RESULTS

Briefly, I will describe the methodology of this demonstration:

I used an insulin syringe, which has a relatively small volume gradient capable of (quite) accurately measuring 0.01 ml of milk, and I added the milk into 50 ml of water, which result in very diluted solution. Then, the dilution was poured into a glass vial which was shined by a bright pseudo-white L.E.D light source. This enables me to capture the light, that was scattered from the particles contained in the milk using my Nikon D5000.

By varying the volume of milk added into 50 ml of water, we are able to adjust the concentration of the dilution. For each dilution I snapped a photograph of the light scattering and transmission (light that passed through the liquid). We can then see the result, how light are being scattered away and transmitted depending on the concentration of the milk.

The picture above shows the interesting result of light, scattered by increasing concentration of milk. Notice as the concentration of milk gets higher, meaning more tiny fat-particles in the water, more blue light is scattered. At about 0.003% concentration, so much blue light was scattered under so much presence of particles, the scattered light was saturated into other wavelengths as well, hence a whitish appearance.

This compilation shows a clearer example of light scattering: it is the transmission of light through the samples of milk dilution. Note the bright light in the center (light that is not scattered to other directions in the bottle) comes from the L.E.D at the back side of the glass vial. Initially, at very low concentration of milk, the colour change in the central light source is barely noticeable, but even at low intensity, the scattered blue colour surrounding the central white light is obvious.

In increasing concentration, the colour of the central light source turn from white to yellowish red, showing more blue light has been scattered away, leaving the red light passing through the milk. It is important to note the "strength" of the central light source starts to dim as the concentration increase because most of the incoming light has been scattered away thanks to the increasing amount of fat-particles suspended in the liquid.

This demonstration clearly shows two points:

1. As more particles suspended in the medium, more light is scattered away, which result in the central light turning from bright white to a dim red.

2. As described by Rayleigh scattering, more blue light is scattered by the fat-particles drifting in water. As blue being scattered away, it leaves only red part of light, transmitting through the milk-water dilution.

COLOURS OF THE SKY

These two points adequately shows the reason why our clear sky appears blue in the afternoon, and the sun shines bright white as compared to the red-hued sun in the evening . Similar to the milk-water dilution, our air contains tiny particulates such as molecules of oxygen, nitrogen, ozone and microscopic dusts which acts as scattering medium.

When we look up to the sky in the afternoon, the distance between your eye to the edge of the atmosphere of earth is shorter compared to looking towards the horizon in the evening. A shorter distance correspond to lesser molecules for the light to scatter upon, thus it is similar to the case of a very diluted milk.

In the evening, light from sun passes through a much larger distance of atmosphere, upon scattering of so much blue light by the molecules in the air, what's left, is a beautiful dim red globe we adore when we decide to put on our running shoes and goes out for an evening jog.

Footnote:

We can think of the energy coming in the form of a wave, scattered by so many individual unit of the medium. The scattering medium is an electronic charge bound to a nucleus. Both the electron and nucleus are thought to be "forced" to oscillate in the same frequency (we call it resonance) with the incoming light-wave which has an alternating electric component.

Now, how the electron behaves in response to the incoming light depends on the frequency of light and also the natural frequency of both potential oscillators. There are two things we need to consider: the electron's natural frequency lies in the UV range, and the molecular vibration lies in the IR region. Because atoms has much higher mass compared to the electron, the strength of the induced oscillation in molecules are much smaller compared to electrons, and thus ignored in this discussion. Calculations have shown, that these induced oscillations are only slightly influenced by the frequency of the incoming light, therefore, we can think of the tiny oscillators are electrons accelerating in harmonic motion. These tiny oscillators are radiators. They are antennas that re-radiate or scatter energy in all directions except on where they receive it.