How does constitution determine the authority …

FIRST things first. Law has to be understood in context of usage. So if it were a democracy with a socialist manifestation of laws, like India: Law has a social purpose. If it were authoritarian regimes, law is a command of sovereign.
Determination of legitimacy or the power of sanction against contravention of laws is the domain of sovereign power. In International Law, every State is sovereign. But within that State, sovereignty to make, execute or enforce laws may lie in the hands of: Executive, Legislature or Judiciary. In  UK, Legislature, the Parliament is sovereign (Parliament of UK can do everything except turning a man into woman and woman into man). Indian Constitution is sovereign.  Legislature, Executive and Judiciary derive their powers, duties from this written document. Thus although traditionally Legislature makes laws, it may be held illegitimate or ultra vires the Constitution by Judicial Interpretation of the Constitution.