That's too tenuous a translation here. With more context it works, of course. If someone asked "Do you have mirror?" and you answered "I have a compact", you are indeed telling that person that you have a small mirror, but to anyone else who didn't hear the question you are simply saying you have a compact.
What do you mean by "nitrous", is that some auto-spelling-correction artefact?
This dictionary thinks so: http://www.oxforddictionaries.com/definition/learner/looking-glass
I'd ask for "looking glass" and "looking-glass" to be accepted if I were you - no harm done.