What instrument has the ability to measure angles down to minutes or even seconds, depending on the accuracy of the instrument?

The theodolite is an optical instrument specifically designed for measuring angles with high precision in both vertical and horizontal planes. Its capability to measure angles down to minutes (1/60th of a degree) or even seconds (1/3600th of a degree) makes it a critical tool in surveying, construction, and engineering applications where accuracy is paramount.

The theodolite achieves this precision through advanced optics and precise mechanical engineering, allowing the user to read angle measurements clearly. This level of accuracy is essential for aligning structures, establishing reference points, and conducting detailed topographic surveys.

In contrast, while the other instruments listed have their specific uses, they do not measure angles to the same degree of precision as a theodolite. The tilting level and optical level are more concerned with establishing level and plumb lines rather than precise angular measurements. The optical square is used primarily for checking right angles and ensuring straight lines, lacking the capacity for fine angular measurement that theodolites provide.