Color II

Color Mixing by Subtraction

In order to subtract certain wavelengths from broad-band white light, one needs filters . Filters are characterized by their transmittance curves, the curves that show what fraction of the incident light is transmitted at each wavelength. When one sends broad-band white light though a filter, the intensity distribution curve of the transmitted light is the same as the filter's transmission curve. It is important to understand tat a filter cannot change the wavelengths contained in the light, just the intensities.

In order to determine the result of mixing two colors subtractively, one must know the transmittance curves of the filters involved. In general, the subtractive rules are complicated. However, for ideal filters, which transmit 100% at some wavelengths and 0% at all others, the laws of subtractive mixing are quite simple.

When white light shines on those filter, they transmit

Combining filters one obtains

How do we understand this?

Transmittance curves of

  1. an ideal blue filter
  2. an ideal green filter
  3. an ideal red filter
  4. Result of a subtractive mixture of any of (a), (b), and (c). Also shown are transmittance curves of filters that transmit the same light as one gets form additive mixtures of (a), (b), and (c).
  5. ideal yellow filter (green + red = white minus blue)
  6. ideal magenta filter (blue + red = white minus green), and
  7. ideal cyan filter (blue plus green = white minus red).
Notice that (a), (b), and (c) also give the results of subtractive mixtures of (e), (f), and (g). For example, a subtractive mixture of (f) and (g) gives (a), as shown schematically in (h).

Simple subtractive mixing rules:

Cyan+ Magenta = Blue
Cyan + Yellow = Green
Yellow+ Magenta = Red

and

Cyan+ Magenta + Yellow = Black

Subtractive Primaries

Choose a filter of blue, green, or red and shine white light through the filter:

White - Blue = Green + Red = Yellow
White - Green = Blue + Red = Magenta
White - Red = Blue + Green = Cyan

Hyperphysics: Subtractive Color Mixing

Subtractive Color Mixing

Subtractive mixture laws for realistic filters and dyes

The simple subtractive rules apply only to ideal filters. They would also apply to ideal transparent dyes. Dyes are substances that absorb certain parts of the spectrum. Mixing transparent dyes also results in a subtractive color color mixture. In general, there are no simple rules that allow to predict the result of a subtractive mixture of real dyes or filters, if one only knows the colors (i.e. chromaticities) of the constituents one mixes. For such subtractive mixing the result depends on the details of the intensity distribution curves, that is on the details of the transmittance curves of the filters or dyes.

To illustrate how complicated eve a simple case can be, consider the mixing of a color (dye) with itself.

  • Transmittance curve of one filter (solid line); of two identical such filters, one behind the other (dotted line)' and of many identical such filters, one behind the other (dashed line). Here, instead of giving the percentage of incident light transmitted at each wavelength, the fraction transmitted is given.
  • Path, in the chromaticity diagram, of the color of the light transmitted as more and more filters are used and the intensity of the incident light is increased proportionally. One filter gives a desaturated orange (point marked 1). Several filters give an unsaturated purple. Many filters result in a monochromatic violet.

    Subtractive color mixing of two different dyes at various concentrations

    (a) Transmittance of blue (1) and yellow (2) dyes at unit concntrations, and (3) a one-to-one mixture of the two dyes, also at unit concentration.
    (b) Chromatricity path as the concentration of mixtures of the two dyes is increased. At very low concentration the dyes are almost transparent, so the illuminating white light passes through unchanged (W). As the concentration is increased, the color becomes more saturated, ultimately becomes red at high concentrations. The path between white and red depends on the ratios of concentrations of the two dyes. Shown are a one-to-one mixture (1:1), a three-blue-to-one-yellow mixture (3:1), and a one-blue-to-three-yellow mixture (1:3). The points marked b and y are the colors of the unit concentration dyes shown in (a). Thus, appropriate mixtures of these yellow and blue dyes result in almost any color in the lower half of the chromaticity diagram, but not the green one might expect from blue and yellow.

    Try it! Subtractive mixtures of color with itself.

    Problem: Lights in a Theater

    Subtractive Color Mixing with Filters

    Dependence of subtractive color on the light source

    The color of the light reflected from an object usually depends on the color of the illuminating light, e.g., gold looks more orange if the light shining on it is itself golden yellow. One can see a more extreme example of this effect under the `golden white' sodium lamps one often finds on highways: some objects lose their color because there is very little green and red light emitted by this source.

    How can one tell what color an object will acquire under a nonwhite illumination? You know that the objects reflectance curve tell what fraction of the incident light is reflected at each wavelength. Hence, if you know the intensity distribution curve of the incident light, you need only multiply it by the reflectance curve to get the intensity distribution curve of the reflected light.

    1. Intensity distribution curve of light from a Cool White fluorescent tube.
    2. Reflectance curve of a magenta object.
    3. The intensity distribution curve of the light from that object under Cool White fluorescent illumination is given by the product (at each wavelength) of the curves (a) and (b). Under this illumination, the object looses all hue.

    Even if two illuminating lights look the same, an object may still appear in different colors in them. If a white light consists of two narrow bands of complementary colors, say cyan and red, objects illuminated by it have only one or the other color, or a mixture of these colors. A yellow object may appear red or black, depending on how broad its reflectance curve is. However, the same object will appear yellow when illuminated by a broad-band white, such as daylight, even though both whites look the same when reflected from a white screen.

    For this reason, when buying clothes, you are often advised to take the material to a window nag look at it by daylight, as well as by the artificial illumination in the store. Even that may be insufficient. Light from the northern sky may be bluish, direct sunlight has its maximum in the green, while the late afternoon light is reddish. All of these lights may look white to you, since the eye adapts to the illumination.

    Intensity distribution curves of white light sources
    1. 100 W incandescent bulb
    2. Delux Warm White fluorescent tube
    3. 400 W high pressure sodium high intensity discharge lamp.
    Objects illuminated by different light sources
    1. sunlight
    2. an Agro-Lite (plant light)
    3. and incandescent light
    4. a `golden white' sodium lamp

    If a light source produces light because it is hot, e.g., an incandescent light bulb or the sun, its color (and consequently the color objects appear when illuminated by it) depend on its temperature. The intensity distribution curves of most hot, glowing bodies are just the black body spectra we encountered in Chapter 6. The hotter the source, the more the relative intensity at the shorter wave lengths. A cool body radiates almost exclusively in the infrared. As it is heated, it begins to glow red. Further heating may make ti yellow, white, or even blue.

    Broad-spectrum sources are often classified by color temperature, the temperature of a black body source whose color matches that of the source in question. Two sources of the same color temperature give off light that looks the same. Of course, colored object may appear differently colored under two such source because their intensity distributions may be different. But almost all incandescent sources of the same color temperature have the same intensity distribution. This is a convenient way of standardizing such light sources. E.g. in TV studios the color cameras are balanced for a standard 3200o photoflood.

    The location of the color of the light from incandescent sources at various temperatures.
    The temperature is in degrees Kelvin (Ko) . Shown are three standard white light sources

    1. tungsten filament (2854o K)
    2. noon sunlight (4870o K)
    3. tungsten filament filtered to approximate `daylight' (6770o K)
    A candle would be about 1880o K, while a photographic flash would be 4300o K.

    • Ch. Elster
    Aug 26 14:27:03 EDT 2019