Final answer:
The phenomenon described is known as induction, which occurs in the lac operon of bacteria when lactose is present, prompting the synthesis of Lac permease and β-galactosidase.
Step-by-step explanation:
The phenomenon where the addition of lactose to a bacterial medium causes a 1000-fold increase in the synthesis of the two proteins Lac permease and β-galactosidase is termed induction. In the context of the lac operon, this induction occurs when lactose is present in the environment, causing allolactose (a form of lactose) to bind to the lac repressor. This binding alters the shape of the repressor so it can no longer bind to the operator, thus lifting the repression and allowing for transcription and subsequent translation of the lac operon's genes including Lac permease and β-galactosidase.