1.10.10.5: Subtractive mixing
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- 128494
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)5.1 Subtractive mixing using coloured filters
One method is to shine a single source of white light through two filters. For example, the following diagram illustrates what might be expected for a magenta filter followed by a cyan filter.
An even simpler method is just to hold the filters between your eye and a light source, perhaps a window.
The following photos show some possibilities using the four different anaglyph glasses that I purchased. The left hand photo shows how they were attached to a window with adhesive tape; the right hand photo provides an enlarged view of the overlap regions between the filters.
The overlap at the top left shows that the subtractive mixing of red and magenta produces red.
The overlap at the top right shows that the subtractive mixing of red and cyan produces black.
The overlap at the bottom left shows that the subtractive mixing of red and green produces black.
The overlap at the bottom right shows that the subtractive mixing of blue and green produces a darker green instead of the black that might be expected. The reason is that these simple filters pass a wide range of wavelengths. Thus the green filter also passes some blue and the blue filter also passes some green.
There are several other possibilities that can be investigated, especially if you have multiple sets of some glasses.
5.2 Subtractive mixing using reflection and filtering.
Objects can appear coloured when viewed in white light because some wavelengths are absorbed (i.e. subtracted) and others are reflected. Thus red paper appears red because only wavelengths that produce the sensation of red are reflected while all the other wavelengths are absorbed. Subtractive mixing can thus be investigated by passing the coloured light produced by reflection through a coloured filter. The diagram belows shows how the reflection from yellow paper might appear when viewed through a green filter.
To investigate the reflections from several different colours I have mounted the Newton disc that was printed and used in section 3.2 on a sheet of white paper.
The photographs below show what was photographed with no filter, a red filter and a green filter respectively.
The photographs below show what was photographed with a blue filter, a cyan filter and a magenta filter respectively.
The subtractive mixing can obviously occur in the opposite order as shown in the diagram below. Here the coloured light is produced by passing white light through a coloured filter before it is reflected. The diagram below shows how the reflection from blue paper might appear when illuminated by light that has passed through a magenta filter.
The photographs below show the results for red, green and magenta filters respectively. As expected, they are very similar to those shown above;
5.3 Subtractive mixing using coloured pigments
The coloured pigments used by artists fall into two main classes
(i) transparent (often inks and watercolours)
(ii) opaque (oils and acrylics)
Here's an example showing how the additive primaries (red, green and blue) can be obtained by mixing the subtractive primaries (cyan, magenta and yellow).
This diagram illustrates how the mixing of two transparent colours (cyan and magenta) on a white background can produce a new colour (blue).
Coloured pigments usually reflect a wide range of wavelengths, and so the results of their mixing can be quite complicated. This will be considered in further experiments.