electromagnetism - Is there is any way to prove the Faraday's law of induction?

I want to know if there is any way to prove the Faraday's law or is it just an experimental observed phenomena?

More specifically, is there any reason why the proportionality constant is 1? How did Faraday discover it? I also heard that we can prove Faraday's law using the principle of least action, but is that true?