Apr 30, 2011

To find the vertical distance between two points using Sextant

Apparatus:
1. A sextant
2. Chalk pieces of two different colors
3. A rigid clamp stand a measuring tape,
4. A plumb line
5. A spirit level
Description of Sextant:
Sextant is an optical instrument as shown in Fig. and is meant to measure angles. It consists of a graduated circular arc about 60° having two radial fixed arms A and B. There is another arm known as third moving arm C (index arm) that moves over the circular graduated scale. It carries a vernier scale V on one side and plane mirror M₁ is perpendicular to the plane of arc. A second mirror M₂ called the horizon glass is fixed to the arm A whose lower half is silvered while upper half is transparent. The plane of this mirror is also perpendicular to the circular arc. A telescope T is fitted to the arm B with its axis perpendicular to the horizon glass. The telescope receives the direct rays through the transparent portion of M₂ and twice reflected rays from M₁ and M₂.
Working Principle:
The distant object is viewed directly through the clean parts of mirrors M₂ and then the movable arm is so rotated that the mirror M₁ and M₂ become parallel. In this position the telescope receives the rays from distant object in two paths

The movable arm containing mirror M₁ is moved such that the rays coming directly from P towards telescope and rays coming through the paths RM₁, M₁, M₂ and M₂T coincide with each other. The angle RM₁Q is the angle between the directions of the two objects, which is twice the angle BM₁C. To facilitate this circular scale is directly marked as twice the actual degrees.
Theory
If h is the vertical distance between two points X and Y and θ is the angle subtended by XY at the index glass M₁ of the sextant at a distance d then
h/d=tan⁡θ
This is true only when M₁Y is perpendicular to XY.
Procedure:
1. Find the vernier constant or the least count of the sextant.
2. Mark a horizontal arrow nearly 10cm long on the wall with a colored chalk at a height of about 1 meter from the floor. Mark another horizontal arrow vertically above it near the ceiling.
3. Place a rigid clamp stand at a distance of nearly 5 meter from the wall. Clamp the sextant in the stand with the scale downwards and the objective of the telescope pointing horizontally towards the lower mar. Adjust the height of the sextant so that the axis of the telescopes horizontal and is at the same level, as the lower mark Y of the ground. Test with a spirit level. With the help of a plumb line adjust the plane of the scale to be vertical. Move the telescope sideways by the screw at its side so that the line of demarcation of the silvered and un silvered portions of the horizons glass M2 lies in the centre of the telescope objective.
4. Focus the telescope on the lower mark Y and adjust the position of the sextant so that the image of the horizontal arrow is in the centre of the field of view. This is the direct image as seen in the telescope.
5. Move the arm CD so that the image of the same horizontal arrow is also visible in the telescope after reflection from the two mirrors. This will happen when the vernier reading is nearly zero and the instrument is in proper adjustment. If the reflected image is not in the field of viewer does not concide with the direct image, the horizon glass is not perpendicular to the plane of the scale. To adjust this, work the small screw provided on the carriage of the horizon glass till the two images lie one above the other. If the two images seen are not of the same brightness, it can be adjusted by moving the telescope sideways with the help of the screw provided at the side of the telescope.
6. When the two images of the mark Y overlap, note the reading on the scale.
7. Keeping the eye in the same position move the arm CD. One-half of the field of view will appear to slide past the other half and ultimately the image of the upper arrow will appear to approach the direct stationary image. Note the scale reading when the two images again overlap.
8. Measure the distance from the lower arrow to the index mirror by a measuring tape.
9. Repeat the experiment with three different distances of the sextant from the lower arrow.