Someone who is imperious is (1) arrogantly domineering or overbearing, or (2) regal. In the first sense the word is synonymous with dictatorial, and it comes from the Latin imperium, which means extreme authority. It is often extended to mean masterly, perhaps due to a misinterpretation of the word as meaning without peer. This use of the word is out of line with the word’s traditional definition, but it’s common enough to be considered a secondary sense
Impervious means (1) incapable of being penetrated, or (2) unaffected. It’s usually followed by to and then the thing to which one is impervious. A bulletproof vest, for example, makes one impervious to bullets, and a hard, nonporous surface makes something impervious to moisture. Pervious is a word, meaning penetrable or open to passage, but it’s much rarer than its im- antonym.
The mainstream media tells us so, with an imperious sneer. [Washington Post]
Harry Anslinger was an imposing figure, husky and nearly six feet tall, with an intimidating stare, an imperious air, and a flair for self-promotion. [The Strength of the Wolf, Douglas Valentine]
Those receiving public assistance … dislike being treated with contempt by imperious government officials. [Waterloo Record]
He speaks with misplaced authority and received wisdom in a place that is far from impervious to manipulation. [Independent]
The water moves downward by gravity until it reaches an impervious layer that prevents it from moving deeper. [Environmental Pollution Control Microbiology, Ross E. McKinney]
Indeed, he seems impervious to criticism of almost any kind except of his remarkable hairstyle. [Economist]