If you were a juror in a criminal trial, how would a judge know if you decided the case on whether......?

When juries deliberate cases, members can ask questions or state their opinions if they choose but are not required to say anything during the entire process unless the foreman decides to use a spoken "Guilty" or "Not guilty" poll or final vote instead of the usual show of hands. Therefore, if you never told the rest of the jury that your vote was based on the fact that you thought the law was wrong (in which case the foreman would be required to report it to the judge, and an alternate would probably be chosen to replace you), the judge would never know your reasoning. Deliberations are secret even from the judge except as far as problems the foreman may report.