[confusedstud]

When anthocyanin is in an acidic medium, its centre ring is aromatic and therefore the entire ring structure is conjugated. While in basic medium, its centre ring becomes non-aromatic breaking up the aromaticity. We know that at a more conjugated system will absorb light of a longer wavelength therefore it would appear bluer than a less conjugated system.

However, anthocyanin in acidic medium (more conjugated) is red while in a basic medium (less conjugated) is blue which seems to contradict the theory about conjugation and colour. Why is that so?

[Corribus]

This isn't really how observed color works. Absorption of photons certainly plays a role in the wavelengths that reach your eyes, but so does scattering and fluorescence. Concentration and solvent also play a role in determining each of these processes. Moreover, the eye doesn't perceive all colors with the same efficiency. So while the absorptive properties of a chemical compound can be predicted, the visual appearance is not necessarily subjected to such simple rationalizations.

Beyond that, while it's true that more conjugation generally results in red-shifting of absorption features, this again doesn't necessarily translate into a change in color that is predictable. For one thing, there can be more than one absorption band that is shifted. But here, take a look at the spectra of anthocyanin at low and high pH, which you can find here:

http://stevegallik.org/cellbiologyolm_Ex01_P04.html

You see that it's true the acidic media results in conjugation so that there is strong absorption in the visible, but the lambda max looks to be around 500 nm or so, and a lot of absorption in the blue region, with plenty of red light (>550 nm) not absorbed. It's hard to tell what the higher pH spectrum is doing in that plot, but you can see there is far less blue light absorbed (as well as other wavelengths), as well as light of other wavelengths. I'm sure based on the absorption spectrum and your eye's sensitivity, you'd be able to explain the observed color change.