Definition: An emergent ray seems to be a refracted beam that originates from a medium or channel after refraction.
Whenever a reflected ray exits glassy slabs, it will become an emergent ray, moving further away from normal as well as parallel just to the incident light. Whenever light travels across two points, an emerging ray would be generated.
When the first light is passed through, it does become a reflected ray, and whenever the subsequent light passes through, it becomes an emerging ray.
Therefore, the emergent ray would be the ray that emerges from a prism, glass slab, as well as mirror following refraction.