I have connected an Apple Superdrive, through a Multiport Adapter, to my new IMac. It doesn't show up in my Finder, and there is no eject button on my computer. How do I eject the disc?

One of the really old ways is still listed in this Apple article:

Eject CDs and DVDs from Mac - Apple Support

Look at the last bullet point: Hold down the mouse button or trackpad clicker while restarting.

The adapter, if not Apple, may be the issue. Many reports here say only Apple adapters work with the basically obsolete SuperDrive (last updated Summer 2012!). They are the only ones that seem to get enough power to the drive.

Are you sure there is a disk in the drive? Even with a fully functional connection, the USB SD must have a drive mounted in it to show in the Finder.

I will apologize in advance for asking the next question. As trite and flippant as it seems on the surface, it addresses the #1 cause of USB SuperDrive problems, so must be asked in this setting where we cannot see your computer. Here goes:

Is the drive "silver side UP."

EDIT: Sorry! Your excellent resolution was not there when I started looking into this.

On occasion, one may eject or remove an optical media disc from a Mac; when invisible

in the Finder, by using Disk Utility to see the item; & use menu tools to eject the media.

Some macOS versions allow one to add an 'eject icon' to the menu bar, nearer day/date;

and items such as these, used to be contained in a system folder within the macOS.

There may be a newer way (or an older different one?) to get past this issue.

With older hardware & software kit, my idea may be outdated by comparison.

Try this Terminal command:

drutil tray eject

followed by the Return or Enter key. You may have to repeat once or twice.

There is always the paperclip method, unless SuperDrives preclude that.

Keith Barkley wrote:

There is always the paperclip method, unless SuperDrives preclude that.

No paperclip-sized manual eject hole on SuperDrive, so, no.