Final answer:
The common interface language used in CORBA is IDL (Interface Definition Language), which facilitates interoperability among objects written in different programming languages by providing a language-neutral interface specification.
Step-by-step explanation:
The common interface language used in CORBA (Common Object Request Broker Architecture) to facilitate communication among objects written in different programming languages is known as IDL (Interface Definition Language). IDL is a language-neutral specification language that defines the interfaces that CORBA objects present to the outside world. CORBA uses IDL to ensure that objects written in various programming languages can communicate with each other seamlessly. IDL provides a precise description of an object's interface, which can then be used to generate language-specific binding code in multiple programming languages, allowing for interoperability across different systems.