Grassmann's law of color and light mixing

On the basis of summarizing the previous experimental phenomena of color mixing, H. Grassman summed up the following experimental laws in 1854, which is called grassmann's law of color mixing and is the basis of establishing modern colorimetry.

Attribute of color (1) Human vision can only distinguish three changes of color: lightness, hue and chroma (or saturation). These three characteristics can be collectively referred to as the three attributes of color.

Brightness refers to the perception of objects by human eyes. The higher the brightness of the luminous object, the higher the brightness; The higher the reflectivity of a non-luminous object, the higher the brightness. Tone refers to the characteristics that distinguish colors. Radiation with different wavelengths in the visible spectrum is visually represented by various tones, such as red, orange, yellow, green, cyan, blue and purple. Chroma indicates the intensity or purity of the color of the object.

In the visible spectrum, monochromatic light has the highest chromaticity, the purest color and the lowest chromaticity of white light. When monochromatic light is mixed with white light, the chromaticity will decrease. The more white light is mixed, the lower the chromaticity is, but their hue remains unchanged. The chromaticity of the color of an object depends on the selectivity of the reflected spectral radiation on the surface of the object. If an object has high reflectivity for a narrow band of the spectrum and low reflectivity for other bands, the color in that band is high.

Complementary Color Law and Intermediate Color Law (2) In a mixed color composed of two components, if one component changes continuously, the appearance of the mixed color also changes continuously, from which two laws are derived: complementary color law and intermediate color law.

Complementary color law: each color has a corresponding complementary color; A color is mixed with its complementary color in an appropriate proportion to produce white or gray; When mixed in other proportions, intermediate colors of color components in approximate proportions are produced.

Intermediate color law: any two complementary colors are mixed.

Intermediate color, its hue depends on the relative number of two colors, and its chromaticity mainly depends on their distance in hue order.

(3) the law of substitution

Similar colors (that is, colors with the same appearance) are still similar after mixing. If color A= color b and color C= color d, then color A+ color C= color B+ color d.

According to the replacement law, as long as the colors are visually the same, they can be replaced with each other. Let A+B = C. If there is no color B and x+y=B, then A+(X+Y) = C. The mixed color produced by this substitution is visually different from the original mixed color.

(4) the law of brightness addition: the total brightness of the mixed color is equal to the sum of the brightness of all the colors that make up the mixed color.

People have long realized that two different colors of light can give people a new color feeling after mixing.

1, CRBT

Experiments show that colors can be mixed with each other to produce a new color feeling different from the original color. Color mixing can be a mixture of color and light, or a mixture of dyes. The former is a mixture of color addition and the latter is a mixture of color subtraction. The results of these two kinds of mixing are different. The following only introduces the additive mixing of colored light.

If the spectral colors with the highest chromaticity are surrounded by a ring in turn, and purple is added, the circumference of the color solid will be formed and become a color ring, as shown in the following figure. Each color occupies a certain position in or on the ring, and the white with the lowest chromaticity is located at the center of the circle. In order to infer the position of the mixed color of two colors, two colors can be regarded as two weights, and this position can be determined by the principle of calculating the centroid. That is to say, the position of mixed color depends on the proportion of two color components, which is close to the color with large proportion.

Two colors that are mixed to produce white or gray are complementary colors. Any two colors at both ends of the diameter of the color ring are complementary colors.

The sound velocity formula becomes

Where is the sound wave velocity and r is the specific heat ratio of air or other diatomic molecules.

Sound intensity level: SIL= 10lg (? / ? 0 )

Reference level? 0= 1pW/m2

Sound power level: SWL= 10lg(Wa/W0)

Reference value W0= 1pW

Sound pressure level: SPL=20lg(p/p0)

Reference value P0=20μPa (in air)

P0= 1μPa (in water)

The human ear can hear the sound of 20Hz to 20 Hz,

Therefore, only an objective and quantitative description of sound is not enough to evaluate its influence on people. When people listen to sound, what they feel subjectively is its strength (loudness), pitch (pitch) and quality (timbre).

Tone is the attribute of hearing to distinguish the sound level, and pitch is another representation. Tone is basically determined by frequency,

The relationship between tone and frequency of pure tone has its regularity. If it is a periodic signal, it is mainly determined by the fundamental frequency.

Sound waves form standing waves in a completely closed space.

Far from being inversely proportional to the square of distance as in free space, the sound intensity at some distant points is higher than that near the sound source.

Glassman's Law is a law used to describe the gradual change of Indo-European pronunciation, which was put forward by Hermann Grassmann to supplement greenman's law.

Green's law has laid a solid foundation for historical linguistics, but it is not impeccable, with a few exceptions. Some exceptions appear in the roots of aspirated stops. For example:

Sanskrit bódh-ati "Attention"

Greek peúth-omai "experience"

Gothic (Germanic) ana-biudan "command, command"

According to Green's law:

Sanskrit b- corresponds to Greek b and gothic p.

Sanskrit Greek Gothic

BP

Gothic b corresponds to Sanskrit bh and Greek ph.

Sanskrit Greek Gothic

bh ph b

Greek p corresponds to Sanskrit p and Gothic F.

Sanskrit Greek Gothic

p p f

As can be seen from the above table, Green can't explain the correspondence of the first consonant. Grassmann thinks that this correspondence is the result of a series of phonetic changes in Greek and Sanskrit, and puts forward a very reasonable explanation: Greek and Sanskrit have the same phonetic phenomenon, that is, if the same word in the original Indo-European language contains two voiced aspirated stops, in Greek and Sanskrit, the first aspirated consonant will become a non-aspirated stop. This is Glassman's law. Because in Greek, the voiced aspirated stops in the original Indo-European language become voiced stops, and under the action of Glassman's law, these stops will become unvoiced stops: * bheudh-> * pheuth-> Persian Sanskrit retains voiced aspirated stops, so these stops become voiced without aspirated stops: * bheudh-> * bho DH-& gt；; Bode.