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I found this Wikipedia page on this property called color index. Unfortunately, I could not find a source that explains this property well.

My interpretation is that color index is the brightness difference of an object through some 2 different wavelengths. Is my understanding correct? If not, could someone explain it to me?

Also, if my understanding is correct, why would there need to be a calibration table, as shown in the above link?

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A colour index measures the ratio of brightnesses in two wavelength intervals, not the difference.

The reason an index is written as the difference between two numbers is due to the logarithmic astronomical magnitude system - the difference between two logarithms is the logarithm of the ratio.

The reason that a red colour is bigger than a blue colour is also because of the perverse way that objects with smaller magnitudes are brighter.

The calibration table you refer to appears to just show that stars of different spectral class and temperature exhibit different colours.

You do however need a calibration to relate real brightness ratios and real properties of stars to the colours. That is because each logarithmic magnitude scale has its own zeropoint (the flux associated with a zeroth magnitude star in that band). The baseline colours are defined using the star Vega as a standard, such that all the colours of an A0 main sequence star are approximately zero (as shown in that table).

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