The correct answer is option 1, Dinabandhu Mitra. The author of `Nildarpan` was Dinabandhu Mitra. Now, let`s dissect the other options to understand why they are incorrect.

Option 2, Sivnath Sastri, is not the correct answer because he was a prominent historian, writer, and social reformer, but he was not the author of `Nildarpan`.

Option 3, Devendra Nath Tagore, is also not the correct answer. Devendra Nath Tagore was a prominent religious and social reformer, but he did not write `Nildarpan`.

Option 4, Harishchandra Mukherjee, is not the correct answer either. Harishchandra Mukherjee was an influential journalist and founder of the newspaper `Hindu Patriot`, but he was not the author of `Nildarpan`.

Therefore, the correct answer is option 1, Dinabandhu Mitra. He was the author of `Nildarpan`, a play that exposed the atrocities and oppressive practices of the British towards the indigo planters in Bengal.