How does a modern DSLR camera and lens actually adjust its aperture

I understand what aperture is and how it applies to photography. Larger F number = less light but more depth of focus, smaller F number = more light but less depth of focus. On an older Nikon lens that I have, there is a little tang on the lens mount that I can move back and forth and will open up the iris. When the lens is mounted to the camera, it is opened up all the way. I understand that this is to aid in focusing through the viewfinder. However, when the camera takes the picture, the iris doesn’t move. I am able to adjust the aperture and take photos, but how is it controlling the “iris”.

A similar thing happens with modern lenes, but I can’t see any iris at all.

So how does a modern DSLR camera and lens actually adjust it’s aperture size?