These values define the quality of the light from a lamp. High-quality light renders colours in the same way as natural daylight with cloud cover around mid-day.

The sun and all incandescent lamps and tungsten-halogen lamps emit light with a spectrum that very closely resembles that of a black body. For this reason, comparing a light source with natural daylight is like comparing it to a black body.

White light can be broken up by a prism into its spectral components. Conversely, adding together all the spectral components of a radiation source produces a colour impression (white, for example, in the case of daylight).
 
Increasing the temperature of a black body produces different spectrums. All the light of these spectrums causes various impressions of colour in the eye of an observer. Imagine a horseshoe in the blacksmith's fire. First it glows red, then yellow as its temperature rises, until finally it is white hot. Each temperature corresponds to a different spectrum and each spectrum corresponds in turn to a location in the colour triangle. If you join up all the locations you get the Planckian Curve.

To determine the colour temperature of a light source the colour location in the colour triangle of its spectrum is compared with the colour locations of a black body at different temperatures.

If the spectrum cannot be compared with that of a black body then the spectrums (of, say, discharge lamps) are assigned to the closest colour temperatures using Judd lines.

Black bodies such as the sun or tungsten-halogen lamps render colours accurately because they emit a continuous spectrum.
If a light source does not emit all colours in a balanced spectrum, some body colours will not be rendered as well as if they were illuminated with a continuous spectrum.

The colour rendering index of a lamp indicates the extent of this deviation from the ideal light source. In a comparison test the remission spectrums of eight test colours, illuminated with the lamp to be tested, are measured and compared with the values of a given reference light source. The colour temperatures of the lamp under test and those of the reference light source should be as close as possible (correlated colour temperatures).

The deviations in the measurements are evaluated using a standardised procedure. If the spectrums of both lamps are identical then the colour rendering index (R_a) will be 100. The index is generally less than this.
The highest possible colour rendering index (R_a=100) is assigned to the black body.