# Integrating math and science -- Dry Ice Fog.

Integrating math and science can be as simple as learning to use a ruler, or as complex as learning multivariate analysis.Correlation is a powerful statistical tool, and it's a great way to learn about integrating math and science.

To learn how to find a correlation, let's say you want to find out ....

Does adding food color to water change the color of the dry ice fog made by that water?

To answer this question you will need to add three different food colors to water. I recommend using red, blue, and green.

Color provides us with information about the wavelength of the light we see. Red is the longest wavelength of visible light, and blue is the shortest. Green sits in the middle of the visible spectrum.

If food coloring affects the color of dry ice fog, we would expect that "red" fog would reflect more red light and less blue light, "blue" fog would reflect lots of blue light and less red light. "Green" fog might have lots of green light, or might be balanced between red and blue.

Computer monitors produce millions of different colors by simply mixing red, blue and green light. We will use that fact in this experiment.

Adobe RGB is widely used to define colors for computers. It uses this system:

Wavelength of pure color (nm):

Red: 610Green: 540 Blue: 465

When looking at "red" fog, we would expect to see lots of light at the long wavelength. So with "red" fog, we might expect that the amount of light will go up with the wavelength. We call this a "positive correlation."

For "blue" fog, we would expect to see lots of "short wavelength" light, and less "long wavelength" light. Thus for blue light we would expect to see the amount of light to go down as the wavelength goes up. We call this a "negative correlation."

Integrating math and science: Collecting color data

Make three different solutions of food coloring, and make dry ice fog with each of them.

Use a digital camera to take 3 pictures of each of the fogs.

Upload the pictures into a computer, and...

Use Photoshop or similar software to collect data from the photos.

Your image is probably already in RGB mode, meaning it is using red, green, and blue. But sometimes, you will need to convert to RGB mode. This is very easy. On most versions of Photoshop, you will select:

Image>Mode>RGB Color.

Then you will need to set things up so you can easily collect data. You will use the Eyedropper tool, and read the data from the Color Window.

First make sure you have a color window open by selecting:

Window>Color

Then click on the eyedropper tool to select it. Now, you can collect data easily, simply click on the picture where there is some fog, and record the amount of Red, Green and Blue in various sections of the fog. I recommend collecting 10 data points from each picture, and taking three pictures for each "color" fog.

Integrating Math and Science: Using a spreadsheet to analyze the data.

Most spreadsheets have great statistical tools for integrating math and science.

As you collect your data, enter it into a spreadsheet. In the first column put the peak wavelength, and in the second column, the amount of color.

Next you will need to see if there is any correlation between the wavelength of the light and the intensity of the color. If you don't have the data analysis tool installed on your spreadsheet, you will need it install it.

This is very easy. Choose:

Tools>Add Ins..., and choose "analysis toolpack."

Now you will need to see if you have a correlation.

Select Tools>Data Analysis, then select "Correlation."

Then you will simply use your cursor to select the two columns of data, tell the spreadsheet to group by columns, and to put the result on a new worksheet.

You will see your results almost instantly. With the data this I collected, there was a negative correlation, but this doesn't mean anything.

You will need to collect more data than I did, and then compare the results of the red, green, and blue. (All three might have a negative correlation, but if red is the least-negative, that would confirm our hypothesis, while also indicating that the room may have more blue light than red light.)