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One of the pieces of feedback the German military got form he invasion of Poland in 1939 was a desire for a squad-level designated marksman in each unit. This would be a man with the best shooting skills of the unit, but not actually a fully trained sniper, and he should be equipped with a light and simple optical sight, for shooting at small targets like pillbox ports or sandbagged machine gun nests. To fill this need, development of what would become the ZF-40 and ZF-41 scope was started. It was initially envisioned as mounting to the G41(M) and G41(W) rifles, although this never actually happened.
Instead, by the time the scopes were ready for use, those fully-trained snipers were deemed a higher priority, and there were insufficient regulations ZF-39 type scopes in production to equip all the snipe