since henna only adds color, on black it won't show at all, but it will have a red shine in the sun light. (depending on the type/quality of henna it can be from a deep red to a light orange color/shine). On the faded coppery parts, it should make a burgundy color (how dark depends on how dark you hair is now). On your natural color, it looks like it should give a light auburn color (assuming its henna with good/deep pigmentation). Since hena only adds color, its going to look how it does now, only with a red/orange cast to your entire hair.
you didn't mention this but i thought I would share to maybe benefit your or someone else:
If you want a more uniform color throughout, you can mix some indigo with the henna and apply it only to the new growth, this will help darken it to match the darker parts of your hair. You can also try repeated applications of henna to the new growth, this will darken the red. It wont match the brown parts, but it will make it less of a contrast.
My hair is henna/indigoed black and im letting my natural color (dark-medium brown) grow out too. Personally i like the darker ends.
Henna will look great on your hair by the way.