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Thermodynamics

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Sextant

Sextant is based on the principle that a reflected ray is turned through double the angle through which the mirror is rotated. It is used to find the height of buildings, mountains and altitude of the sun. it is mainly used by the mariners on the ship to find the altitude of the sun because it is not affected by the motion of the ship.

It consists of a mirror M₁ half of which is silvered and the other half is a transparent glass. The mirror M₂ can be rotated and its position can be read on a circular scale PQ with the help of the vernier V. A telescope T is provided to view the two images side by side, one through the transparent glass and the other reflected by M₂ and M₁. The instrument is used to read the altitude (angle) directly. The circular scale PQ is marked such that each half degree on the scale is marked as one degree which is usually 60˚ is marked 120˚.

When the reading is zero, both the mirrors M₁ and M₂ are parallel and the their planes are perpendicular to the plane of the arc PQ.

1. Height of a building: A horizontal lien A is marked at the base of the building whose height is to be determined. The line is marked at the same level as the eye of the observer. The index arm CD is kept vertical and is rotated such that the line A seen directly from the transparent glass M and the image of A reflected BY M₂ and M₁ lie side by side. This will be so, when a continuous line is seen in both the parts on the scale is noted. Rotate the index arm and bring it to a position such that the top of the building (B) reflected by M₂ and M1 and the lien A as seen through the transparent glass of M₁ lie side by side as seen through the telescope. Note the reading of the vernier. Find the angle through which the index arm has been rotated. Let it be equal to θ₁. Now, move back by 10 meters and again repeat the experiment. Suppose the angle in this case = θ₁.

Let the height of the building be h.

Cot θ₁ = AE/h

Cot θ₂ = AF/h

As EF is known, h can be calculated. Similarly, the height of a mountain can also be calculated. In order to calculate the area of a window, the height and breadth of the window are found with the sextant. To find the breadth, the sextant is kept such that the index arm CD is horizontal.

2. Altitude of the sun: A dish containing mercury is taken. The telescope of the sextant is directed towards the mercury surface and the index arm CD is rotated such that the image A₁ of the sun in the mercury as seen through the transparent glass of M₁ and after reflection from M₂ and M₁ lie side by side. Note the reading of the vernier on the scale. Rotate the index arm CD such that the image of the sun formed by reflection from the mirror M₂ and M₁ coincide with the image of the sun in mercury as seen through the transparent glass. Find the reading through which the index arm rotated. Half of the reading gives the altitude of the sun. Here a mercury surface is used instead of a mirror because it sets itself horizontal under the action of gravity.