The correct answer is option 3, Deen Bandhu Mitra. Deen Bandhu Mitra is the author of the play "Darpan" which was written in the year 2010. It is important to note that Deen Bandhu Mitra was a renowned Bengali playwright, poet, and novelist of the 19th century.

Option 1, Aurobindo Ghosh, is incorrect as he was not the author of the play "Darpan". Aurobindo Ghosh was a philosopher, poet, and nationalist from India, but he was not known for writing plays.

Option 2, Bankim Chandra Chattopadhyay, is also incorrect as he was a novelist and not known for his plays. He was the author of the famous novel "Anandamath" and is considered one of the key figures in Indian literature.

Option 4, Rabindra Nath Tagore, is not the correct answer either. Although Tagore was a prolific writer and playwright, he did not author the play "Darpan" in 2010.

Therefore, the correct answer is option 3, Deen Bandhu Mitra, as he is the author of the play "Darpan".