How can a supernova be used to measure distance?
Supernova Type 1A are typically referred to as "standard candles" and can be used to measure distance due to their constant energy explosions.
Type 1A supernova occur when a white dwarf has reached the Chandrasekhar limit of 1.4 solar masses. Since the supernova always occurs at this point and mass is equivalent to the amount of energy that could be contained in the supernova, each supernova will have the same brightness.
If an object is space has the same brightness and this brightness is known, then how bright it appears gives an immediate determination of the distance to the object.
So in the case of supernova, by looking at how bright the supernova appears and knowing exactly how much energy it contained, we can figure out at exactly what distance it is at.
In general, the distance goes as