20mm (.7 inches roughly) glass signal mirror the size of a 20mm button compass

Would a signal mirror this small be effective at signaling up to 5-10 miles? I read on this site somewhere that size plays a role in distance, is there a rule of thumb on size for distance?

If I cut down a piece of old mirror and polished up the edges, coated the back in rubber and packed it along would it be almost as effective as my traditional signaling mirror, minus the aiming hole of course?

The reason I ask is the Rat Cutlery fire steel has a small capsule built into the handle that would fit something like this, I think it would be very handy to be able to fit compass, mirror and whistle in this little compartment. I could probably stuff the remaning space with a vacuum sealed cuben fiber tarp to take the place of an AMK heatsheet for wind and rain protection.

What do you guys think, ludicrous?

Also, have you ever seen anything manufactured this small?