How does extracellular glucose inhibit transcription of the lac operon?

The lac operon is a set of genes in bacteria (E. coli) involved in lactose metabolism. The genes are expressed when lactose is present and glucose is absent.

There are two regulators of the operon: the lac repressor and catabolite activator protein (CAP). The lac repressor is a lactose sensor which usually blocks transcription of the operon. When lactose is present the repressor stops acting as a repressor. Another regulator is metabolite activator protein (CAP) which is a glucose sensor. It activates transcription of the operon when glucose levels are low. When glucose levels are low, cAMP is produced. cAMP binds to CAP which then binds to DNA and promotes transcription. When the glucose levels are high, there is no cAMP and CAP cannot bind to DNA-low transcription (or no transcription, depending on lactose).