The correct answer is option 2 - Sir Thomas Roe. Sir Thomas Roe arrived in the court of Jehangir as an official ambassador of the King of England.

Option 1 - William Hawkins was an English adventurer and naval commander, but he did not arrive in the court of Jehangir as an official ambassador.

Option 3 - Sir Edward Terry was an English chaplain and author, but he also did not arrive in the court of Jehangir as an official ambassador.

Option 4 - Bernier, also known as Francois Bernier, was a French physician and traveler who visited India during the 17th century. However, he was not an official ambassador of the King of England and did not arrive in the court of Jehangir as such.

Therefore, the correct option is 2 - Sir Thomas Roe, who arrived in the court of Jehangir as an official ambassador of the King of England.