1.10.10.3: Partitive mixing of light in time

In this type of mixing the light from different sources is not present simultaneously at the same point in space, rather the light from different sources falls sequentially on the same place. Providing this occurs more rapidly than the response time of the photoreceptors in the eye, the effect will be the average of the various sources.

3.1  Partitive mixing using alternating sources of light.

In this experiment uses a red/green LED unit that has an individual red and green LED connected ‘back to back'. This means that it is impossible for both LED to be working at the same time.

When connected to a DC source with one polarity the LED will be red.

 

       

When connected to a DC source of the opposite polarity the LED will be green.

        

If connected to a supply of alternating polarity (an AC voltage) the unit will alternately display red and green. If this occurs more rapidly than the photoreceptors in your eye can respond, you will see the average of the two light sources. The left hand photograph below shows the LED driven by a small AC voltage. It was photographed at a slight angle so the individual red and green LED can be seen within the unit. The right hand photograph shows what happens when a much larger AC voltage is applied. The alternating red and green, although never present simultaneously, are combining to produce yellow. (Although a 50 Hz voltage works for the eye, we had to use a higher AC frequency for these 2 photographs).

            

The intensity of the light from each LED depends upon the current flowing through it. The following circuit allows the brightness of each LED to be controlled by adjusting the 100k potentiometers. By reducing the current to the green LED relative to the red LED we can produce orange as seen in the photograph.

         

So far we have been using a 50 Hz AC supply, and accordingly the red LED will flash once during the positive part of each cycle and the green LED will flash once during the negative part of each cycle; consequently there will be 50 red and 50 green flashes each second. Because we see the combination as yellow, this rate must be faster than the response time of the photoreceptors. The circuits below allow us to control the rate at which the red and green flashes of light occur, and thus allow us to investigate the response time

 

Here is a movie showing what happens as the AC frequency is increased.

The distinct red and green flashes gradually combine until a yellowy-green colour results. A problem arises here bcause the optical characteristics of a digital camera are very different from the human eye – the response time of the camera is much faster. Here I have used a very low effective ASA rating and the lowest possible light levels so the simple point–and–shoot camera required as long an exposure time as possible. There can also be problems with frequency of the flashes beating with the frame rate. This exercise looks much better in real life rather than in this video.

3.2  Partitive mixing using spinning discs to reflect light.

While he was a student, the great physicist James Clark Maxwell became intrigued by the color tops used by James David Forbes, his professor. By rapidly spinning the top, Forbes created the illusion of a single color from the several colours present on the disc. Maxwell took the coloured spinning tops invented by Forbes, and was able to demonstrate that white light would result from a mixture of red, green and blue light, and that virtually any colour could be produced by adding these additive primaries. There are several ways you can repeat these experiments.

(a) use a commercial top

(b) make a simple top – here I have used an old CD mounted on a pencil.

(c) Modify a personal, battery–operated fan. These are available for A$2 to A$3. Simply remove the fan blade, and use a flexible adhesive to attach a plastic disc, I've found that the tops of takeaway sauce containers are ideal for the rotating disc.

(d) use a power tool. A high speed electric drill or similar works well.

WARNING: You should always use eye protection when high speed electric tools are used.

Traditionally experimenters have used the reflections from coloured cardboard and/or paper. However the ready availability of excellent inkjet colour printers means that is easy to produce coloured discs in virtually any colour.

Here are links to files that will allow you to print out sets of suitable coloured discs on A4 paper (if possible use high quality photo paper). The larger discs are a suitable size for mounting on a CD, the smaller ones will fit the top of a takeaway sauce container. They will produce a set of discs in the additive primaries (red, green and blue), and the subtractive primaries (cyan, magenta and yellow). A slit should be cut in each disc so that they can be rotated with respect to each other and their relative areas thus varied.

      

Use these links to download the files for printing.

Large red and green discs   DISC-CD-RG-Print.pdf

Large magenta and cyan discs  DISC-CD-CM-Print.pdf

Large blue and yellow discs  DISC-CD-BY-Print.pdf

Small discs in all colours   DISC-TA-CMYK Print.pdf

Here's an example of combining red and green. You won't produce a bright yellow because the reflected red light is only present half of the time, and so is the green light; consequently you are effectively mixing their combination with black.

Here's an example of combining red and blue.

Maxwell used spinning tops to perform a quantitative study.  He used an approach whereby the colour produced by mixing two or three colours on the outside of the disc could be directly compared with the colour produced by different colours on the centre of the disc. This doesn’t require any colour memory and the comparisons are made under the same lighting conditions. This allowed the formulation of equations that describe colour mixing. Thus for the example shown below one could write that

0.5 red + 0.5 green = 0.44 yellow + 0.56 black

   

You can try this approach yourself using the large and small printed discs.

Newton showed that white light could be decomposed into a continuum of colours. He developed a colour circle to explain the colours produced when different colours add.  Unfortunately the number of colours (seven) was based on mystical considerations and the relative areas of the colours were assigned by analogy to the musical scale. These colours have been superimposed upon the colour wheel from Newton’s “Opticks”

Consequently although it was an very original idea, it doesn’t quite work, e.g. the summing all the colours on the disc should produce white. You can try this yourself by using the small Newton disk on the printer files.

 

3.3 Partitive mixing via reflection.

It is also possible to use reflection to partitively mix light.

If the sea were beautifully flat with a mirror–like surface, two different coloured light sources would be seen as separate reflections. However the surface of the sea is usually covered by small ripples and waves that are caused by the wind, passing ferries and yachts, sharks, etc, etc.

The photographs below show an example of how the reflections of a red and a blue advertising sign can add to produce a magenta reflection. It was taken late at night when I was walking after another great concert from the Sydney Symphony Orchestra at the Sydney Opera House.  I used a hand–held camera, hence some blurring. The right hand photo was taken using telephoto.

      

This example of partitive mixing probably occurs both in time and space.