Submitted by: Deepali JainDevendra Kumar SharmaDilip Kumar MeenaDheerendra maharya

(E&C – A), B- tech, Ist Year

Submitted to:Physics Department, Jagannath Gupta Institute of Engineering and Technology

Supervised by:-

Dr. Pranav Saxena

SEMINAR COVER’S

1. Object 2. Apparatus3. Description of sextant4. Principle 5. Theory6. Procedure7. Observations8. Calculations 9. Result10. precautions

Object

To Determine the height of a given object by using Sextant

Apparatus :

Sextant

What is Sextant ?

A sextant is a navigational instrument used to measure the angle of elevation of celestial bodies, usually the sun or moon, in order to determine one's location and direction.

More generally, a sextant can be used to measure the angle between any two objects, by which we can calculate the distance between them.

Parts of a Sextant

Index mirror: large polished plate that reflects light.

Telescope: optical instrument made of lens that magnifies objects.

Telescope clamp: reinforcing circle.

Eyepiece: lens the user looks through.

Telescope printing: lens adjustment.

Frame: structure that serves as the base for the different parts of the sextant.

Graduated arc: graduated edge of the arc.

Locking device: apparatus that holds the sextant in place.

Drum: graduated button used to take measurements.

Index arm: type of ruler that determines direction or measures an angle.

Screw to regulate small mirror: piece of metal used to adjust the horizon mirror.

Glass filter: colored transparent substance.

Horizon mirror: small polished glass plate that reflects light.

Glass filter: colored transparent substance.

Sextant is based on the principle of rotation of a plane mirror . According to this principle, When a plane mirror is rotated through an angle , the reflected angle is rotates through an angle 2 provided that the incident ray remains unchanged

Principle of Sextant:

ᶿᶿ

Theory :

αβ

Let H be the height of the water tank MQ whose height is to be determined. Take a refreance point P on MQ at a height hr above ground

PQ = MQ – MP = H – hr = h

Let α and β be the angles subtended by the PQ height at F and E , distance apart.

. . cot ∙ α = ― PEPQ

PE = h cot α . PQ = h∙ ∙

Similarly cot β = ― PFPQ ∙. PF = h cot ∙ β

β α

∙. X = Pf – PE ∙

= h ( cot β – cot α )

h = X .cot β – cot α

∙.∙ Actual height of water tank

H = h + hr

H = X .( cot β – cot α )

+ hr

Procedure:1. Find the least count of the vernier attached with the index arm. 2. Draw a horizontal line P as a reference line on the pillar of the water tank.

3. Look at the horizontal line P through the transparent portion of the horizon glass plate M2 by telescope from some distance (say 10 m) from the water tank keeping the plate of the arc scale of sextant vertical .

4. Rotate the index arm towards zero of the scale till direct image of reference line P coincides with the image of the same reference line through the polished portion of horizon glass plate M2

5. Now rotate the index arm away from zero reading till the image of the top Q of water tank in the mirror M2 coincides with the image of the reference line P seen directly through the glass plate M2 .

6. take 3 sets of the observations at different distances.

Least count of circular scale = 1'

Observations:

Least count of micrometer screw = 1°

Least count of vernier scale : 1/5' = 60/5= 12"

Height of Sextant from ground hr = 5 ft

Observation table:-

Sr. no.

Distance Zero Reading (a) Elevation reading (b) Angle of elevationѲ = b-a

M.S C.S. V.S. Total M.S. C.S. V.S.

total

1. 7 m 3° 33' 2" 3.56° 12° 26' 2" 12.41° α = 8.862. 9 m 3° 19' 2" 3.317° 10° 38' 2" 10.63° β = 7.317

3. 11 m 3° 27' 3" 3.45° 9° 31' 2" 9.51° ϒ = 6.066

Calculations:(i) x = 9m – 7m = 2m

α = 8.866° β = 7.317°

h1 = x .cot β- cotα = 2 .

7.787 – 6.415= 1.485 m

(ii) x = 11m – 9m = 2 m

2 .h2 = 9.433 - 7.787

= 1.233 m

ϒ = 6.066°β = 8.866°

(iii) x = 11m – 7m = 2

ϒ = 6.066°α = 8.866°

H3 = 4 .9.433 - 6.415 = 1.325 m

(H') mean = h1+ h2+ h3 .3

= 1.347m

H = hr + H' = 5 + 4.42 ft = 9.42 ft

1.347 x 3.28 ft = 4.42 ft

Result:Height of water tank is 9.42 ft

% error = Calculated height- Actual height Actual height

x 100

9.42 – 9.00 =9.00

x 100 = 4.7%

Precautions:

Plane of index arm should be parallel to the moving arm and normal to the plane of the circular arc.

At the position of zero reading both mirrors M1 and M2 should be parallel to each other.

While taking reading the plane of the fixed arm and index should be kept vertical.

The telescope should be directed towards the centre of horizon glass M2.

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