The 11th-century Persian scholar who wrote about Deepavali in his memoir on India was Al Biruni.
Abu Rayhan Al-Biruni was a Persian polymath whose interests included astronomy, mathematics, chronology, languages, religion, and history. He spent years studying the Indian subcontinent and learned enough Sanskrit to engage with Indian intellectual traditions directly. His major work on India is commonly known as Kitab al-Hind, or Al-Biruni’s India.
In this account, Al-Biruni described Hindu beliefs, social practices, scientific ideas, calendars, and festivals. He noted that Deepavali was celebrated on the new-moon day of Kartika, helping preserve evidence about how the festival was understood in the early 11th century. His approach was unusually analytical for its period, even though his work naturally reflects the limits and assumptions of a medieval observer.
The alternatives belong to different contexts. Ibn Battuta was a 14th-century Moroccan traveller, Al-Idrisi was a 12th-century geographer, and Firishta was a much later Persian historian. None is the scholar associated with this specific description.