Why things are coloured

White light contains all visible wavelengths (about 400–750 nm). A substance that absorbs part of that range removes those colours, and the light it transmits or reflects looks like the complementary colour, the one opposite on the colour wheel.

• Absorbs blue light (435–480 nm): looks yellow.
• Absorbs nothing in the visible: colourless (white as a powder).
• Absorbs across the whole visible range: black.

In a conjugated molecule the absorption promotes an electron from the HOMO to the LUMO, so the gap $\Delta E = hc/\lambda$ decides which colour is absorbed.

β-Carotene has 11 conjugated C=C bonds (22 π electrons), a long enough system for the HOMO–LUMO gap to fall in the visible: $\lambda_{\max}$ = 450 nm. Its absorption is a broad band covering violet, blue and some blue-green light (about 400–500 nm). Removing that whole range leaves yellow, orange and red light, which we see as orange. (Looking up 450 nm alone would suggest yellow; the width of the band matters.)

Lycopene, the red pigment of tomatoes, also has 11 conjugated C=C, but in a flat open chain. It absorbs further into the blue-green ($\lambda_{\max}$ ≈ 470 nm) and looks red. In β-carotene the two C=C inside the end rings are twisted out of the plane, which slightly shortens the effective conjugation.

Short conjugated systems have large HOMO–LUMO gaps and absorb only ultraviolet light, so they look colourless: ethene (171 nm), 1,3-butadiene (217 nm), benzene (255 nm), 1,3,5,7-octatetraene (290 nm), even 1,3,5,7,9-decapentaene (334 nm).

A simple polyene needs many conjugated double bonds before $\lambda_{\max}$ passes 400 nm, which is why β-carotene, with 11, is coloured and hexatriene, with 3, is not. Sunscreen molecules use this: they are conjugated enough to absorb harmful UV but not visible light, so they are colourless on the skin.