Assertion (A) is true: The marine sextant is an optical instrument used by navigators to measure celestial altitudes (vertical angle of the sun, moon, or stars above the horizon) and horizontal angles between landmarks to determine geographic position at sea. Reason (R) is true: It operates on the optical principle of double reflection between an index mirror and a horizon glass; because the angle between the mirrors is doubled by two reflections, its arc of one-sixth of a circle ($60^\circ$, hence 'sextant') measures angles up to $120^\circ$, precisely explaining how it functions as an angular measurement tool.

Option analysis:

• Both (A) and (R) are true and (R) is the correct explanation of (A): Correct, double reflection optics explains its design and measuring range.
• Both true but not explanation: Incorrect, (R) directly explains the optical working mechanism of (A).
• is true but (R) is false: Incorrect, (R) is true.
• is false: Incorrect, (A) is true.