This is brilliant acting right here. You can see the EXACT moment he sees Harry and realizes that he has his mother’s eyes. You can see what Snape was thinking; the moment he sees Harry, he probably just thought that he was going to be arrogant, immature, and exactly like how James Potter used to be.
But then Harry turns his face and looks at him. They make eye contact, and the realization hits him like a ton of bricks. He has Lily’s eyes.
And let’s not forget this was the first movie. Bravo Alan Rickman.