The ability that adult peregrines possess is not gained without a great deal of practice. Watching the young birds acquire that skill, from playfighting with one another to chasing their parents as the latter bring food in, is one of the great sights of summer. Week by week you can see the transformation from awkward learner drivers to confident young fighter pilots. An hour or two watching them, once they have gained some expertise, trying to find out just how high the sky is will really make you appreciate good optics.
I think the build-up to the stoop and the start of it can be almost as dramatic as the end. You know from the steadiness with which the tiny dot in your 10x is circling that she is not just ranging around her territory, but looking with the eye of the perfect huntress, better by far than Swarovision, at everything that flies below; then she's accelerating, wings flickering before being folded tight as the black teardrop streaks down from the sky. Have you seen them change gear as they come down? I've been smoked many a time when a bird I thought was coming down fast turned on the afterburners and simply vanished from my vision. "A falcon towering in her pride of place", "She stoops to conquer", etc. If only the Bard had had binoculars.