Should I Focus on the Front Sight or the Target?
With traditional pistol iron sights, sight alignment is critical, so visual attention generally needs to favour the sights rather than trying to keep the target perfectly sharp. It is normal for the target to appear less sharp. The exact visual strategy can vary with discipline, eyesight and sighting system, but attempting to see the target, sights and everything else perfectly sharply at once is not realistic.
Why alignment matters
A small angular error in the relationship between front and rear sight continues downrange. That is why sight alignment deserves the larger share of your visual attention.
Do not chase the target
The target provides the aiming reference. The sights provide information about where the pistol is pointing. Your job is not to visually force everything into perfect stillness.
Eyesight changes with age and some shooters use corrective lenses or aperture devices. If your visual strategy has stopped working, that is worth investigating with an optician who understands shooting.
Glossary
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Always follow firearm-safety rules, range regulations and the manufacturer's instructions. Safety takes precedence over training.