Final answer:
The sextant is a navigational tool that measures the angle between two objects, such as the Sun and the horizon, using double reflection. It is crucial for maritime navigation and has replaced older instruments like the cross-staff and backstaff. The surveyor's telescope, similarly, is used for measuring angles for surveying and mapping purposes.
Step-by-step explanation:
The instrument described, used for measuring the angle between two objects using double reflection, is known as a sextant. A sextant is equipped with a sliding scale that is a fraction (1/6) of a full circle, which justifies its name. It allows navigators to 'shoot the Sun' by measuring the angle from the horizon, using the sharp contrast provided by the sea's horizon as a reference. The ship's officer aligns the image of the Sun and the horizon in the instrument's view to determine this angle accurately, which is vital for navigational purposes such as estimating latitude.
Historically, the predecessor of the sextant was the cross-staff, used by navigators such as Columbus to gauge celestial angles by elevation. However, due to the problem of direct sunlight, the backstaff was developed, which directed sunlight onto a target rather than into the observer's eye. The sextant's double reflection design allowed for more precise measurements without direct eye exposure to the Sun.
Another important tool for measuring angles in surveying is the surveyor's telescope or theodolite. This instrument measures the azimuth angle and enables the telescope to be pointed in any direction to record angles with respect to geographic directions, contributing to land surveying and mapmaking accuracy.