Mirror of Erised Question

So I'm rereading Harry Potter and the Sorcerer's Stone. I've gotten to the chapter "The Mirror of Erised" and to the part where Harry discovers the mirror. The following excerpt is what my question is about.

"The Potters smiled and waved at Harry and he stared hungrily back at them, his hands pressed flat against the glass as though he was hoping to fall right through it and reach them."

Okay so... why just the Potters? Why not also the Evans-es? I mean, it's revealed a little later in the book that what Harry desired was his family so that's the the mirror showed him. But... it just showed him the Potters, not the Evans-es.

I have no explanation for this, only a small theory: Harry already thought he knew what his mother's side of the family was like so he didn't really want to see them.

I'm pretty sure Lily and Petunia's parents were dead before Harry was born and so he never got to meet his grandparents. I'm sure Mr. and Mrs. Evans wouldn't have been as nasty to Harry as Petunia and Vernon were. That's why I say Harry thought he knew.

Anyway... that's my random tangent for today.

Love ya, Jessie