Why does butan-2-ol have no effect on plane polarised light?

Butan-2-ol can be produced as a result of reducing butanone with NaBH4. The hydride ion in NaBH4 is used as a nucleophile which can attack the C on the (C=O )either above or below the plane, depending on the orientation of the double bond. A dative covalent bond is formed. The double bond (C=O) is broken as electrons are transferred to the oxygen, leaving it negatively charged. There is thus an electrostatic attraction between the O- ion and an H+ ion, ultimately producing butan-2-ol. As the nucleophile can attack from above or below the plane, there is an equal probability that each of the two enantiomers of butan-2-ol will be produced in equal amounts, thus generating a racemic mixture. Regardless of the chiral centre in butan-2-ol, the equal amounts of opposing enantiomers means they will rotate plane polarised light in different directions by the same amount - cancelling their individual effects. Butan-2-ol is therefore not optically isomeric in this instance.