Can you make a sunset in a cup of milk?
Published: September 23, 2015
Yes, you can make a sunset in a cup of milk. The same orange and red pattern of colors that you see when the sun goes down can be created in your cup of milk if you set up the situation properly. The physics that makes your cup of milk orange and red is the exact same physics that makes the sky at sunset orange and red. In this sense, you can literally make a sunset in your cup of milk. You don't even need the sun to do it. Let's look at the basic physics first and then we'll understand how to make a sunset in a cup.
When light scatters off of an object that is much larger than its wavelength, the light acts just like a little marble. Because of this, the different colors of light all bounce off a large object at the same angle. This type of scattering is called "geometric scattering". It is the type of scattering that we are most familiar with in everyday life. Red light has a wavelength of 630 nanometers. In contrast, the diameter of an apple is about 8 centimeters, which is about 130,000 times larger than the wavelength of red light. Therefore, red light definitely bounces off an apple geometrically.
Since white light consists of all visible colors, shining white light on an object that is much bigger than the wavelength of the light causes the different colors to all reflect at the same angle. This leads to two effects when a big object is illuminated by white light: 1) the object has the same color no matter what angle it is viewed at, and 2) the overall color of the object is largely determined by which colors are and are not absorbed. For instance, a maple leaf is much larger than the wavelength of visible light and thus causes light to scatter geometrically. A healthy maple leaf absorbs red, orange, yellow, blue, and violet light from the full spread of colors that are present in the incident white sunlight. Therefore, the leaf only reflects back green light. We see the leaf as green since this is the only color of light that reaches our eyes. Furthermore, the leaf looks green from all viewing angles. Since the color of a large object is mostly determined by its absorption spectrum, which is typically constant for all objects made out of the same material, the color of a large object is the same for all objects in the same class. For instance, all the healthy leaves on an oak tree are green. Because color is constant across all viewing angles and across all objects in a class when optical scattering is at work, humans tend to think of color as an innate property of an object, which is a helpful but inaccurate oversimplification.
In contrast to geometric scattering, Rayleigh scattering involves the scattering of light off of objects that are much smaller than the wavelength of the light. When light scatters off of such an object, the light does not act like a marble striking and bouncing off a point on the surface of the object. Rather, the light acts like a vibrating uniform electric field that completely encompasses the object. As a result, the light scatters in all directions to some extent. Furthermore, the amount of light that scatters in a certain direction depends on the color of the light and not on the object's surface geometry. This leads to two effects when a small object (smaller than about 100 nanometers) is illuminated by white light: 1) the object has a different color depending on what angle it is viewed at, and 2) the color of the object is not determined by the shape or surface material properties of the object.
What is the pattern of color generated by Rayleigh scattering? An object displaying Rayleigh scattering scatters mostly blue and violet colors in the sideways direction, leaving red, orange, yellow, green, and reduced amounts of blue and violet to continue traveling in the forward direction.
Since small objects don't scatter very much light, and since humans can't see small amounts of light, it takes a large collection of small objects in order for humans to see the light produced by Rayleigh scattering. Furthermore, the objects have to be fairly spread out so that they act like independent objects. If a collection of small objects are closer to each other than the wavelength of light, they will just act like one giant object. So, where can we find a large collection of nanoscale objects that are somewhat dispersed? In the atmosphere and suspended in liquids.
When you think of small objects dispersed through the atmosphere, you probably think of dust particles, bits of pollution, raindrops, droplets of mist, and the small droplets of liquid water that make up clouds. It turns out that compared to the wavelength of visible light, all of these objects are far too big to participate in Rayleigh scattering. Instead, these objects mostly generate geometric scattering, which tends to scatter all colors equally in all directions. For this reason, dust, pollution, rain, mist, and clouds tend to be white, or variations of white such as gray or brown. The objects in the sky that are small enough to display Rayleigh scattering are the air molecules themselves, which are mostly nitrogen molecules (N2) and oxygen molecules (O2). Each air molecule scatters blue and violet colors the most in the sideways directions and lets the other colors continue on in the forward direction. That is why the daytime sky is blue (the daytime sky does not look violet for several reasons, the main one being that human eyes do not see the color violet very well). Around sunset, there is so much air between the sun and the observer that the blue colors have already been scattered to other parts of the earth, leaving mostly the red and orange colors.
Milk is mostly a collection of tiny protein-coated blobs of oil suspended in water. These blobs are small enough to generate Rayleigh scattering. Therefore, by shining light through a glass of milk, you can get the same color effects as in the sky. However, regular milk has such a high concentration of these oil blobs that each light ray scatters many times before exiting the cup. Each series of multiple scattering events tends to randomize and average away the color effects of Rayleigh scattering. As a result, a cup of milk at regular concentration just looks white. In order to see the color effects, you need to dilute the milk. This will cause the oil blobs to spread out enough that the light rays only scatter once.
Take a clear glass cup with a smooth surface and fill it almost to the top with water. Next, add milk to the cup one drop at a time. After adding each drop, mix everything together and look at a bright light bulb through the cup. Keep adding the drops of milk until the light bulb appears red or orange when viewed through the cup. Presto! You have a sunset in a cup. To heighten the effect, do this at night with all the lights turned off except the one light bulb you are looking at through the cup. Next, position yourself so that you are looking at the side of the cup relative to the line connecting the cup and the light bulb. You now see a blue color. Presto! You have the daytime sky in a cup.