The sextant is an instrument used in navigation for measuring the angle of elevation of the sun or stars. It consists essentially of a fixed glass B, silvered on a vertical half, and a silvered mirror O which can be rotated about a horizontal axis. A small fixed telescope T is directed towards B.
Suppose that the angle of elevation of the sun, S, is required. Looking through T, the unsilvered half, of B, and also the view of it, H, seen by successive reflection at O and the silvered half B, are coincident. The mirror O is then parallel to B in the position M1, and the ray HO is reflected along OB and BD to enter the telescope T. the mirror O is now rotated to a position M2 until the image of the sun, S, seen by successive reflections at O and B, is on the horizon H’, and the angle of rotation, Ө, of the mirror is noted.
The ray SO from the sun is now reflected in turn from O and B so that it travels along BD, the direction of the horizon, and the angle of deviation of the ray is thus angle SOH. But the angle between the mirrors M2 and B is Ө. Thus, from our result for successive reflections at two inclined mirrors, angle SOH = 2Ө. Now the angle of elevation of the sun S, is angle SOH. Hence the angle of elevation is twice the angle of rotation of the mirror O, and can thus be easily measured from a scale which measures the rotation of O.
Since the angle of deviation after two successive reflections is independent of the angle of incidence on the first mirror, the image of the suns through T will continue to be seen on the horizon once O is adjusted, no matter how the ship pitches or rolls. This is an advantage of the sextant.
You can read more on the design, use and principle behind the use of a sextant by following this link