Which school of thought in jurisprudence focuses on analyzing law as it is and applying existing legal rules?

C. Analytical

The Analytical school of thought (also known as legal positivism) focuses on the law as it is, rather than what it ought to be. A judge concerned with interpreting and applying existing legal rules would align with this school, as it emphasizes the systematic analysis of legal concepts and the literal application of enacted law.

• The Sociological school focuses on the social impact and context of law.
• The Historical school emphasizes the evolution and traditions behind legal rules.
• "Ideological" is not a recognized formal school of thought in jurisprudence in this context.

The final answer is $\text{C}$.