Computer Colour Matching Questions and Answers

Answer: A

Correct answer: the colourant concentrations needed to reproduce a target colour

The system works backwards from the target: given a measured standard and a calibrated set of colourants, it computes what concentrations of which dyes or pigments will reproduce it. Predicting the colour of a known recipe is the forward problem, which is the easier half and is used inside the calculation.

Answer: B

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason gives the mechanism. Predicting colour from a recipe is a direct evaluation; predicting a recipe from a colour requires that relationship to be run backwards, and it has no unique solution - many combinations reach the same target. The software must therefore search and then rank, rather than simply compute.

Answer: C

The K over S function is approximately additive across colourants. That linearity is what makes the inversion tractable at all. Reflectance itself would not behave so simply. The transformation is essential to the method.

Answer: D

Correct answer: one minus R squared, divided by twice R

\[ \frac{K}{S} = \frac{(1-R)^2}{2R}. \] The value of this transformation is that it is very nearly proportional to colourant concentration and additive across colourants, which reflectance itself is not. It is what makes the whole calculation tractable.

Answer: A

Both are true and the reason gives the reason, and the transformation is applied wavelength by wavelength. Working directly in reflectance would give quite wrong answers. Addition is valid only after the transformation.

Answer: B

Correct answer: 1 and 2 only

Statements 1 and 2 are the working assumptions of the method: \( K/S \) adds across the colourants in a mixture, and the calculation is carried out independently at each of the sixteen or thirty-one measured wavelengths. Statement 3 is exactly what is not true - reflectances do not add, which is why the transformation is needed at all.

Answer: C

Textile dyeing on a white substrate is the classic case for the assumption. The substrate supplies all the scattering and the dye supplies the absorption. Textile dyeing on white is the classic case. The substrate supplies the scattering there.

Answer: D

Paints and plastics contain scattering pigments and require both coefficients. Determining two constants demands considerably more calibration work. Pigments scatter as well as absorbing. Two coefficients are needed for each of them.

Answer: A

The choice depends on whether the colourant scatters as well as absorbs. Using the wrong formulation gives predictions that are systematically wrong. The colourant type decides which applies. Scattering colourants demand the fuller theory.

Answer: B

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason gives the mechanism. Single constant theory assumes the substrate provides the scattering and fits only \( K \) for each colourant, which suits transparent dyes on textiles. Two constant theory fits both \( K \) and \( S \), which is necessary for pigments that scatter as well as absorb - and doubles the calibration work.