"To the best of my knowledge, they're not mages, no.  ...I'm kind of surprised I didn't accidentally do anything with that Wizardology book I had when I was a kid, but then, I had already been disbelieving...  And the 'wand' it came with probably wasn't actually magic."

"That's not unlike some stories I've heard about muggle-spring mages.  Hard to make a wand if you don't know what you're doing... but you can do some simple things without one sometimes... and now that I think about it, reacting against something that might subconsciously feel like a threat to your mind isn't unlike it either..."

"Well, a test."

She pulls another wand out of her pocket and hands it to Mira.  "Here, this wand should be the least customized.  Best to step out of the circle to minimize interference for a test - not that it should matter, but - anyway, here's a simple light spell:  Hold your wand up like a candle, trace an overhand knot in the air, then jab up, and that'll give you a light."

She demonstrates, and on top of her wand there appears a small yellowish-blue light looking rather like a candle.

Trace a whatnow?  Nevermind, get out of the circle, she's pretty sure it goes like this and this and this and this and jab -

...Why does she have to hold it like a candle, that feels so wrong to her finely-tuned holding pencil-like objects instincts...

Mira feels something moving inside her fingers, something like drops of water running down them.

And on top of the wand, there's a light!

"...Huh.  That felt interesting."

"Yeah, I've heard other people's first wanded magic does too!

"And - congratulations!"  She throws up her hands.

"This answers all our questions and raises new ones!"

"Like what?  And how does magic work, anyway?"

"Like, how did you not realize you had magic till now!?  How many other muggle-sprung mages - or, hey, their mage children who technically aren't muggle-sprung - are walking around not knowing it either!? 

"And - what're you going to do with yourself now that you do know you're a mage!?"

"Lack of opportunity, probably?  It's not like I was usually waving sticks around in real life.  And my guess is, a lot?  It seems like something you could miss just because you're not really...  Looking?

"And, uh, I don't know?  I'm doing a programming sort of degree, I have no idea if that skillset is transferable..."