Emerge means to come forth, to rise up, to come into sight is usually followed by from: “Sachin Tendulkar emerged from the dressing room to give his fans an elusive sighting.”
Immerge, on the other hand, means to plunge or to sink into and to disappear; while in its former meaning, it is synonymous with immerse: “The doctor has instructed to immerge in the pills in water and then feed them to the patient.”
“The faint moon will immerge into the shadow of the sun.”
The mermaid decided to immerge herself into the deep water; then with a flick of her tail, she seemed to emerge from the water like a flash of silver.
