For a compound having n, pi & pi* orbitals (e.g. carbonyl group), it can undergo n-->pi* and pi-->pi* tansitions.
The absroption wavelength (lambda maximum) of n-->pi* is longer than that of pi--pi* as the energy gap between n & pi* is smaller than pi & pi*.
Under polar solvent, the absorption of n-->pi* will shift to shorter wavelength while for pi-->pi* will shift to longer wavelength because the polar solvent stabilizes these three orbitals in different extent, n > pi* > pi.
The reason for this stabilizing effect from my lecture note is that the pi* orbital is more molar than pi orbital (just concern about pi & pi* at this moment) as polar solvent stabilizes polar substances more.
However, I don't know why pi* orbital is more polar.
In my opinion, there is interaction between pi/pi* orbital and orbitals from polar solvent molecules which generates new MOs which are more stable. Moreover, the interaction is much better for pi* orbitals than pi orbital.