Understanding light in terms of physics is very important before discussing about chromatography.  White light such as the sunlight reaching the earth is composed of several colored lights.  In 1666, Isaac Newton passed a narrow beam of sunlight through a prism, and discovered a spectrum, which is arrangement of colors from red to violet as shown in the diagram below.

Each color in the spectrum is associated with a different wavelength of light.  The wavelength of red light is about 700 nm, and violet is about 400 nm.  Thus, rest of color lie between 400nm to 700nm.

      Various colored light was obtained from white line, however it does not require all color shown in spectrum to have white light.  Correct intensities of red, green, blue light are enough to produce white light.  When two colored light are mixed, three new color of light are formed.  They are cyan (red and blue), yellow (red and green) and magenta (blue and green).  Red light, blue light and green light are referred as the primary colors of light, and cyan, yellow, and magenta are called the secondary colors of light.  Additive process among primary colors is widely used. For example, a color television tube is made with many pixels of red, blue, and green light.  And their intensities play a role to create vivid colored images. 

      Think color of light in terms of absorption and reflection.  An apple is red because it reflects red light to observer’s eyes when white light falls on it.  Likewise, dye is a molecule that absorbs certain wavelength of light and transmits or reflects others.  Let’s go over examples of additive process again.  A cyan color is observed due to the reflection of red and blue but absorption of green light.  Likewise, magenta color is from absorption red color but not blue and green.  Finally, a yellow color is from absorption of blue but not red and green. 

What is black color then? Well, it is also mixture of many colors but the primary colors.  When magenta, yellow, and cyan are mixed in certain proportion, black color is observed as a result.  Therefore, black ink is made up with secondary colors. Thus, black ink pens vary depending on different manufactures.  TLC chromatography is a method to separate compounds (ink in this case) from one another without altering them.  It uses solute, solvent, and a medium that molecule will travel along.  In order to get noticeably good results, right solvent for the specific solute must be used.  Since we know ink is from organic compounds, ethanol is right candidate to dissolve them.  As the solvent moves up, the ink molecules will move with it if they are more strongly attracted to the solvent molecules than the molecule of the medium, paper or silica gel.  However, if the ink molecules are more strongly attracted to the paper than the solvent, they will move slowly or even not at all.  Depending on how many different types of molecules are in the solute, all may move at different rates.  Each separated spot can be assigned a Retention Factor (R_f).  It shows the characteristic of specific dyes associated with it.  The R_f is a ratio between distance the dye travels over  the distance of solvent travels.  This ratio should be constant under same chromatographic conditions such as medium, and solvent. 

Above diagram and equation are examples of how retention factors are retrieved and being used in chromatography.