What technological aspect was crucial for revealing Jupiter's faint companions beyond mere magnification?

Resolution, the ability to separate distinct points of light

The ability to resolve distinct objects, rather than simply magnifying them, was the critical differentiator in Galileo's observation. While he certainly improved magnification and clarity in the spyglass, the text specifies that resolution—the capacity to visually separate two very close points of light—was necessary. If the faint companions had merely been magnified without adequate resolution, they would have merged with the overpowering light emanating from Jupiter itself, rendering them invisible to the scrutiny required for scientific verification. This ability to discern separate entities is what transformed the instrument from a simple viewing aid into a scientific tool capable of revealing new worlds.