The correct answer is option 1, Henry Vivian Derozio, who was the founder of the Young Bengal Movement. The Young Bengal Movement was a socio-cultural and intellectual movement that emerged in the early 19th century in Bengal, India. This movement was led by a group of progressive-minded young intellectuals who sought to challenge the orthodoxies and conservative traditions of society.

Option 2, David Hare, was an important figure in the field of education in Bengal and played a significant role in the development of institutions like Hindu College (now Presidency University). While he had a profound impact on education in Bengal, he was not the founder of the Young Bengal Movement.

Option 3, Dwarkanath Tagore, was a prominent businessman and philanthropist during the 19th century. He was not involved in the founding or leadership of the Young Bengal Movement.

Option 4, Prasanna Kumar Tagore, does not have any notable association with the Young Bengal Movement or its founding. Therefore, option 4 is not the correct answer.

In conclusion, the correct answer is option 1, Henry Vivian Derozio, as he was indeed the founder of the Young Bengal Movement.