5Optical and Surveying

Instruments

5.1 IntroductionThe importance of optical instruments has been increasing in the industrialand scientific world for about two centuries. The demands of precision, aswell as of cheap and rapid production, have led to the adaption of opticalmethods in many branches of engineering today. Such methods can be usedin a variety of ways, from tool inspection on the one hand, where meticulousaccuracy is of paramount importance, to certain types of final inspection onmass-produced articles where a reasonable degree of accuracy has to becombined with speedy operation. The instruments based on the optical prin-ciple are being used in the field of surveying and navigation. In this chapter,the basic operating principle of certain types of optical and surveying instru-ments have been discussed.

5.2 MicroscopeA microscope may be defined as an instrument for viewing close objects. Inorder to increase the apparent size of an object, we bring it closer to the eye,but the unaided eye cannot focus on an object which is nearer than a certaindistance which is the minimum distance of comfortable vision. The value of250 mm is universally recognised as the standard minimum distance of com-fortable vision. At this distance, a pair of lines separated by less than about0.1 mm is seen not as a pair but only as a single, broadened line whichrepresents the limit of visual resolution, and it depends on the objects, thecondition of observation and on the quality of the lens. The theoretical reso-lution is given by the formula

Resolution = sin

l

h

K

N(5.1)

where K = a constantl = wavelength of the lightN = the refractive index of the medium surrounding the objecth = half the total angular size of the entrance object (pupil) as seen

from the object.

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The product N sin h is termed as the Numerical Aperture (NA) andcannot exceed the value 1.0 when the object is in air. The value of NA isgreater than 1.0 only for an object which lies in a medium other than air.

5.2.1 Magnification of MicoroscopeThe magnification of a microscope may be defined as the ratio of the angularsize of an image seen through the instrument to the angular size of an objectseen with the unaided eye at the least distance of comfortable vision. If theimage is projected on to a screen, the magnification m is given as:

m =Linear size ofimageLinear size of object

(5.2)

5.2.2 Types of MicroscopesFollowing are the three general types of microscope in common use:

(i) Simple microscopes (monocular)(ii) Compound microscopes (monocular or binocular)

(iii) Stereoscopic microscopes (binocular).

The Simple Microscope The simple microscope is an instrument usedfor viewing close objects with a single optical system. This is popularlyknown as a magnifying or reading glass.

Construction and Working It consists of a single positive (converging)lens which is used close against the eye. The function of the lens is to allowthe eye to focus on an object nearer than the least distance of comfortable(distinct) vision. Figure 5.1 shows a simple microscope in which L is a lensand MI is the least distance of comfortable vision. An eye E cannot seeclearly an object O without the aid of the lens L. For clear vision, themaximum angle is subtended at the eye by the object when it is placed at I. Ifthe object is brought nearer to the eye, the subtended angle a would belarger, but the image would not be clear because MI is the least distance fordistinct vision. But, with the aid of the lens L, the image of the object OP isformed at IR and both the object and the image subtend the same angle at theeye placed close to the lens. Thus, the image appears both distinct andmagnified.

R

PP ¢

E

L

a0I

Lens Eye

Fig. 5.1 A Simple Microscope

MObjectImage

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Magnification of the Simple Microscope The magnification of a simplemicroscope is the ratio of the least distance of distinct vision to the focallength of the lens. If the focal length of the lens is f, the magnification isgiven as:

m = least distance of distinctvision

fbut, as the least distance of distinct (comfortable) vision is 250 mm,

m = 250f

(5.3)

Limitations In a simple microscope, the lesser the focal length the greateris the magnification. However, since the curvature of the surface increaseswith increase in focal length of the lens, it is not possible to obtain a lens ofvery small focal length. As a result a large magnification cannot be obtainedfrom a simple microscope.

Compound Microscope The limitation of a simple microscope is over-come in a compound microscope. In a compound microscope, to obtain alarge magnification, first of all the magnified image of an object is obtainedwith the help of a lens, and then with the help of another convex lens moremagnification is obtanied. Thus, the total magnification is obtained at twostages, which is very large.

Construction and Working A compound microscope consists of two con-verging (convex) lenses, L1 and L2, spaced apart and fitted co-axially in atube as shown in Fig. 5.2. The lens L1 near the object OP is called objectlens (or objective), and the lens L2 near the eye is called the eyepiece. Thefocal length and aperture of the objective are small while they are relativelylarger for the eyepiece. The two lenses are adjusted in a tube in such a waythat the image IR formed by the objective L1, works as an object for theeyepiece and its magnified image I ¢ R¢ is seen at the least distance of distinctvision D. As illustrated in Fig. 5.2, OP is an object placed in front of the

L1

L2

P E

M2

1st Image

I

ObjectiveR

Eye

Eyepiece

2nd ImageLeast Distance ofDistinct Vision (D)

Fig. 5.2 The Compound Microscope

OObject

M1I ¢

Condenser

R ¢

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objective L1, away from the focus. An image IR is formed by the objectivewhich is a real, magnified and inverted image of the object OP. Now, theeyepiece is so adjusted that the image of IR is formed at the least distance ofdistinct vision (I¢ R¢) for an eye placed just behind the eyepiece. This imageis virtual, magnified and erect with respect to IR, but inverted with respect tothe object OP.

Since virtually no microscope object is self luminous, a means is providedfor illuminating it. For transparent objects, a condenser is used whose pur-pose is to concentrate a cone of light on to the object. It must be capable ofproviding a cone of light at an angle which will fill the objective lens so asto make use of the full numerical aperture (NA) of the objective. In practice,the best results are usually obtained with a cone of light equal to about threequarters (3/4) of the objective NA.

A practical compound microscope used in industries is shown in Fig. 5.3.This compound microscope is provided with a fine-focusing adjustment, therange of which is of the order of a millimeter. Only one tenth of this range isnormally used because the coarse adjustment is used to bring an object undera high-power objective very nearly into exact focus. These focusing adjust-ments move the body tube which has a standard length of 160 mm. Theeyepieces are made to a standard diameter which slides into the upper end of

Binocular Eyepieces

Binocular BodyCoarse Focusing

Adjustment

Quadruple RotatingNosepiece

Fine FocusingAdjustment

ObjectivesMechanical Stage

Limb

Condenser

Clamp for Axis Joint Iris Diaphragm

Foot Piller

Fig. 5.3 Practical Compound Microscope

Mirror

Body Tube

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the body tube. The objectives are provided with screw thread and fit into theaperture of a revolving nosepiece or objective changer. The object, normallymounted on a glass slip 75 mm ´ 25 mm, is held by clamping fingers on thesurface of the mechanical stage. Just below the mechanical stage, controlsare provided for moving the object in two directions, at right angles. Scalesand Vernier, on the motions permit the recording of the position on theobject of a particular detail and measuring. A condenser is mounted belowthe stage which carries an iris diaphragm for controlling the angle of illumi-nation, and both are carried into a centring mount which allows the unit to beaccurately centred to the objective. The whole unit can be focused by a rackand pinion on dovetail, in the same way as the coarse focusing adjustment.

Types There are two types of compound microscope:(i) Monocular and

(ii) Binocular.The basic prinicple and construction of monocular and binocular micro-

scopes are the same; the only difference is that the binocular is fitted with abinocular head which consists of two eyepieces, as shown in Fig. 5.3. Themonocular and binocular bodies are interchanged on a special slide fittedwith a cam-locking device which ensures positive and accurate alignment ofthe optical axis. Adjustment for interocular separation is provided and oneeyepiece has the facility for individual focusing to adjust any difference inthe eyes of the observer.

The optical system of the binocular body is shown in Fig. 5.4. A beam oflight from the objective is divided into two equal parts (beams), one to eacheyepiece, by the centre prism, and the remaining prisms direct the light alongthe two eyepiece tubes. Since the path travelled by the light is longer than inthe monocular tube, two correcting lenses are provided to correct for this

Fig. 5.4 Binocular Body.

Outer Body

Right Angle Prisms

Adjustable Eyepiece Non-adjustable Eyepiece

Objective

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difference. The prisms and lenses do not cause any image deterioration, andtheir surfaces are coated to reduce reflection losses and maintain maximumimage brilliancy. The two tubes of the binocular microscope are movable tofacilitate changing their separation to fit interpupillary distance of the ob-server. There is usually an arrangement for individual focusing of one of theeyepieces. The non-adjustable eyepiece is focused in the usual way by mov-ing the tube on the coarse- and fine-adjustment mechanisms, and then thesecond eyepiece is focused to the individual eye.

Inclined bodies are sometimes furnished on binocular microscopes so thatthe objectives is vertical for the examination of liquids, etc. This is madepossible through the use of another inclining prism between the right-angleprisms (dividing set) and the objective. This inclining prism bends the beamof light through an angle of 45° but does not invert the image.

The advantage of a binocular microscope is that eye strain is completelyeliminated, and the inclination of the eyepiece tubes gives comfort and con-venience in working with the instrument in the vertical position.

Magnification Compound Microscope The magnification ‘m’ of thecompound microscope is given by the ratio,

m = Size of the finalimage

Size of the object

or m = ¢ ¢I ROP

(from Fig. 5.2)

But, ¢ ¢I ROP

= IROP

´ ¢ ¢I RIR

or m = m1 ´ m2 (5.4)

where m1 = IROP

Magnification due to objective.

m2 = ¢ ¢I RIR

= Magnification due to eyepiece

Therefore, the total magnification is the product of the magnifications ofthe objective and the eyepiece.

The Stereoscopic Microscope The stereoscopic microscope is essen-tially a binocular instrument of low power used for observations where thethird dimension, depth, is of importance.

Construction It consists of two similar compound microscopes of lowpower with their axes inclined at an angle of about 15°, as shown in Fig. 5.5.The spacing is such that the axes intersect on the focal point. Two prisms areprovided to give erect images to avoid a pseudoscopic effect. These prismscan be rotated about the entering axes for adjusting the eyepiece separation.In research type of stereoscopic microscopes, inclined eyepiece tubes areprovided and the nosepiece carries three pairs of parfocal objectives whichare shrouded for protection. The stand can rapidly be split into sections so asto adapt the instrument for special purposes.

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Uses Stereoscopic microscopes are used for the following purposes:(i) They are generally used as surgical microscopes to aid the surgeon in

certain delicate operations.(ii) They are also used in the adjustment and assembly of small mecha-

nisms and in the checking of small components.

5.3 TelescopeThe telescope is an instrument through which objects situated at large dis-tances can be seen. Because of the distance from the observer, the apparentsize of the object under observation becomes small and the telescope in-creases the visual angle of the final image without altering the accommoda-tion of the eye. Telescopes may be classified into two classes:

(i) refracting telescopes(ii) reflecting telescopes

In refracting telescopes, the objective consists of a converging system oflenses of large focal length and large aperture, while in reflecting telescopesthe objective is generally a paraboloidal mirror. Here, only refracting tele-scopes will be discussed in detail.

5.3.1 Refracting TelescopesRefracting telescopes are mainly of three types:

(i) Astronomical telescope(ii) Terrestrial telescope

(iii) Galilean telescope

Astronomical Telescope The astronomical telescope was developed inthe year 1911 by a Danish astronomer, Kepler, and that is why it is alsoknown as the Keplerian telescope.

Construction and Working It consists of two converging lenses, an ob-jective O and an eyepiece E which are mounted co-axially in a tube, asshown in Fig. 5.6. The objective O has a large aperture and a large focal

Fig. 5.5 Optical System of Stereoscopic Microscope.

Eyepiece

Prism

Objective

Object

Objective

Prism

Eyepiece

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fe fo

Eye

Pa

aE b

Q

O

EyepieceObjective

Fig. 5.6 Astronomical Telescope

length, while the eyepiece E has a short focal length. Since the objective hasto collect sufficient light from the distant object, its aperture must be suffi-ciently large. Thus the eyepiece should also be large to receive all the rayscoming from the objective. When parallel rays from a distant object becomeincident on the objective, the first image PQ which is real, inverted withrespect to the object, and small in size is formed at the focal plane of theobjective. The image PQ is finally magnified by the eyepiece E.

To adjust the telescope for normal vision, the telescope is focussed toinfinity and the position of the eye E is adjusted so that image PQ is formedat its focal plane. Thus, the rays emerging from the eyepiece E will all beparallel and the final image which is magnified, virtual and erect with re-spect to the first image is seen infinity by the eye placed behind the eyepiece.In this case, OP is the focal length fo of the object and EP is the focal lengthfe of the eyepiece. Thus, for normal adjsutment, the tube length of theantronomical telescope should be (fo + fe).

To see the image of an object at the least distance of distinct (comfort-able) vision the eyepiece E is slighlty pushed towards the objective so thatimage PQ is formed within its focal length fe. A virtual and magnifiedimage, which is inverted with respect to the object, is formed at the leastdistance of distinct vision.

When the object is situated at a finite distance, the first image is formedbeyond the focal plane of the objective O and hence, for clear vision of thefinal image, the eyepiece is slightly pulled away from the objective.

Magnification of Astronomical Telescope The magnification (or mag-nifying power) of the astronomical telescope is defined as the ratio of theangle subtended by the image at the eye to the angle subtended by the objectat eye. Thus, from Fig. 5.6, the magnification m is given as:

m = b

awhere b = the angle subtended by the image at the eye

a = the anlge subtended by the object at the eye

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or m = tantan

//

b

a= =

PQ EPPQ OP

OPEP

But OP = fo, the focal length of the objectiveand EP = fe, the focal length of the eyepiece.

\ m = ff

e

o(5.5)

When the instrument is adjusted to form the final image at the leastdistance of distinct vision D, the magnification is given by

m = 1o e

e

f f

f D

+ (5.6)

Terrestrial Telescope Terrestrial telescopes are used for observing terres-trial objects, e.g. in navigation, surveying, etc. where an erect image is es-sential. Since an inverted image is produced by an astronomical telescope, itcan not be used for the observation of terrestrial objects. In the terrestrialtelescope, a convex lens is added to the eyepiece so as to convert the in-verted image into an erect image.

Construction and Working Figure 5.7 show a diagram of a terrestrialtelescope in which a convex lens L is placed between the objective and theeyepiece in such a way that distance of the image PQ from the lens L istwice the focal length (2 fL) of the lens L. Thus, a real and erect image P1Q1equal to the size of PQ is formed at the distance 2fL on the other side of thelens L. The eyepiece E is adjusted so that the image P1Q1 is formed justwithin its focal length and a virtual magnified image P11Q11is seen at theleast distance of distinct vision.

Q11

Q1P11P

E P1

Q

Eye

L Convex lens

Eyepiece2fL 2fL

Objective

Fig. 5.7 Terrestrial Telescope.

Since an extra erecting lens is used in the terrestrial telescopes, the costand size of the instrument is increased. Also, absorption of light will be morein the optical system. The length of the instrument is also inconvenientlyincreased due to the addition of an erecting lens.

Galilean Telescope The disadvantage of the large length of a terrestrialtelescope is avoided in the Galilean telescope. The convergent eyepiece is

O

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replaced with a concave eyepiece. This telescope gives an erect image with-out the use of an erecting lens.

Contruction and Working It consists of a convergent lens (objective) Oof large focal length and a concave lens E as eyepiece, as shown in Fig. 5.8.The concave lens E (eyepiece) intercepts the rays coming from the objectiveO before they reach the image PQ, and so the rays emerge from it as apractically parallel pencil. The eye sees a virtual, erect and magnified imageP1Q1 at infinity, provided the distance EP is equal to the focal length of theconcave lens E. The distance EP is the focal length of the eyepiece E whilethe distance OP is the focal length of the objective O.

P1

Q1 PO E

QObjective Concave Eyepiece

Fig. 5.8 Galilean Telescope.

Since the eyepiece of the Galilean telescope is a divergent lens, the imageis practically formed only by those rays which pass near about the centre ofthe lens, the marginal rays being mostly lost. As a result of this the finalimage is faint, i.e the field of view is limited. Due to this limitation, theGalilean telescope is not generally used.

5.4 Optical SquareThe optical square is an instrument used in surveying to find out the foot ofthe perpendicular from a given point to a line, and to set out right angles at agiven point on a line in the field. It is particularly useful in the case of off-sets which are too long to allow their direction to be judged by the eye alone.

5.4.1 ConstructionAn optical square consists of a small cylindrical metal box, about 5 cm indiameter and 12.5 cm deep, in which two mirrors M1 and M2 are placed at anangle of 45° to each other and at right angles to the plane of the instrument.A diagrammatic view of an optical square is shown in Fig. 5.9(a). The mirrorM1, known as the horizon glass, is half-silvered and half-unsilvered, whilethe mirror M2, known as the index glass, is wholly silvered. The horizonglass M1 is fitted in a frame which is rigidly attached to the bottom plate of

Optical and Surveying Instruments 185

Metal Box 45°

M2Mirror

75°

75°

30°60°60°

60°

h1 h2

h3

COE

D D¢

90°Mirror

(a)D

C(b)

D¢

C¢

Index Glass

Horizon Glass

(c)

Fig. 5.9 (a), (b) & (c). Principle of Optical Square.

the box, while the index glass M2 is fitted in a frame which is attached to thebottom plate and adjusted by a special key placed behind it, whenever neces-sary. In some instruments, the mirrors are permanently fixed by the makerand so cannot be easily adjusted. Three openings are provided in the rim ofthe box and cover: a sight hole h1 for the eye, a small rectangular window h2for horizon sight opposite to h1, and a large rectangular window h3 for indexsight at right angles to line joining h1 and h2. The whole instrument assesmblyis provided with a metal cover which slides round to cover the openings andthus protects the mirrors from dust when not in use.

5.4.2 Working PrincipleThe optical square belongs to reflecting instruments which measure anglesby reflection. The working principle of an optical square may be stated asfollows:

“If there are two plane mirrors whose reflecting surfaces make a givenangle with each other, and if a ray of light in a plane perpendicular to the

M1

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planes of both the mirrors is reflected successively from both, it undergoes adeviation of twice the angle between the reflecting surfaces”. In other words,the angle between the first incident ray and the last reflected ray is twice theangle between the two mirrors. In the case of the optical square, the anglebetween the two mirrors is 45°, while that between the first incident ray andthe last reflected ray is 90°.

As shown in Figure 5.9 (a), the eye E is positioned at sight hole h1 and theobject at C is observed through the lower unsilvered part of the mirror M1.Usually, EC lies along the chain line and C is the pole towards which thechain line was being ranged. An object D is placed at the large rectangularwindow h3, approximately at right angles to EC. While looking from thesight hole h1, a ray of light from the object D, on the line DM2, strikes theindex glass (M2), and is reflected along M2M1. The reflected ray again strikesthe silvered portion of the horizon glass M1 and is reflected along M1E.Thus, the object D is seen at C directly through the unsilvered portion of thehorizon galss M1 and at the same time the image of the object D is seen inthe top silvered portion of the mirror M1. When the angle DOC is exactly90°, the image of D will be seen immediately above that of C [Fig. 5.9(b)],the rays being as shown by full lines in Fig. 5.9 (a). When angle D’OC is nota right angle, however, the image of D’ will be seen to one side of C [Fig.5.9(c)], the rays being as shown in dotted lines in Fig. 5.9(a).

If D is a fixed point and it is required to find where the perpendicularfrom this cuts the chain line, the optical square is held to the eye while thesurveyor walks along the chain line towards C. When the two images appearon the same vertical line, the point immediatelybelow the instrument will be the foot of the per-pendicular required. The optical square must bekept horizontal when observations are being made,so its use is restricted to moderately level ground.

An optical square used in surveying is shownin Fig. 5.10. In some optical squares, prisms arealso used in place of mirrors. Fig. 5.10 Optical Square.

5.4.3 UsesThe optical square is used in surveying work for the following purposes:

(i) To find out the foot of the perpendicular from a given point to a line.(ii) To set out right angles at a given point on a line in the field.

(iii) To determine rectangular off-sets which are more than about 50 metres.(iv) For overcoming obstacles to measurement along a chain line.(v) For determining the area of a plot where perpendicular off-sets are

required.

5.5 Prismatic CompassPrismatic compass is an instrument commonly used for measuring angles insurvey work. It measures the angle, called the bearing, between the magneticmeridian and the line. It is very useful for rough survey work where speedand not accuracy is the main consideration.

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5.5.1 ConstructionA prismatic compass, shown in Fig. 5.11, consists of a circular metal boxabout 6 cm to 16 cm diameter, in the centre of which a circular disc attachedto magnetic needle and graduated to degrees and half degrees (30¢) or evenless than half degrees (20¢) is balanced on an agate bearing. The disc can beraised off its bearing when not in use to prevent undue wear. The gradua-tions on the disc start from zero, marked at the south end of the needle andrun clock-wise so that 90° is marked at the west, 180° at the north, and 270°at the east. At one edge of the box a hairline sight vane consisting of ahinged metal frame is fixed, which may be folded down over the dial whennot in use, while diametrically opposite to this is fixed a prism which mayalso be folded over on the outside edge of the box. A small spring knob isprovided for damping the oscillations and quickly bringing the needle to restwhile taking a reading. The graduations of the scale on the dial, when re-flected to the eye from the hypotenusal side of the prism, can be read bymeans of the prism. The prism can be adjusted to the eyesight of the ob-server by means of a stand by raising or lowering the frame carrying it. Thegraduations of the scale are slightly magnified owing to the shorter sides ofthe prism being made a little convex. A spring is provided near the hinge ofthe metal frame so that the needle is automatically raised from its pivotwhenever the frame is folded over the dial. The top of the box is covered

Adjustable Mirror

Horse Hair

Hinged Sun Glass

Eyevane

Object Vane

Lifting Pin Prism

Glass Cover

Knob Spring Brake Magnetic DiscFocussing Stud

for Prism

Lifting Lever NeedlePivot

HingedStrapCompass Box

Fig. 5.11 Prismatic Compass

Prism Cap

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with a glass lid so that the whole dial with graduations is visible. Alterna-tively, a dial may have a metal cover that reveals only the small area underthe prism. This cover also protects the instrument from dust. Sometimes darkglasses are provided when sighting a luminous object or taking sun observa-tions. Some instruments are provided with a mirror which can be adjusted toany angle in a vertical plane and can be slid on the hinged frame whichcarries the hair line sight. With the help of a mirror, an object of consider-able elevation or depression can be sighted directly by relfection.

The compass is generally held in the hand, as near as possible over thestation point at which an angle is required, but for better results it is usuallymounted on a tripod which carries a vertical spindle in a ball and socketjoint, to which the box is screwed. With the help of this arrangement, theinstrument can be quickly levelled and also rotated in a horizontal plane andclamped in any position. A general view of a prismatic compass used forsurvey work is shown in Fig. 5.11.

5.5.2 WorkingTo determine the angle (bearing) of a line AB from station A, the compass iscentred over station A and levelled. Now the eye is positioned over the slit inthe prism-holder and the prism is lowered or raised in its slide until thegraduations on the dial reflected in the prism are clearly visible.

The hair line is directed to the object (or ranging rod) at station B and, byturning the compass box, the circular disc attached to the needle is allowedto swing freely into the meridian. When the needle comes to rest, the readingat which the hairline appears to coincide with the object is noted. Thisreading gives the required bearing of the line AB. The object and the gradu-ations can be seen simultaneously.

When the bearing of the line AB (i.e. direction of the needle) points duemagnetic north, the reading under the prism should be 360° (i.e. zero) sothat, in consequence, the 360° graduation of the disc is placed at the southend of the needle. Similarly, when the needle points due east, the prismwhich would be on the western side of the dial during the observation shouldbe over the 90° graduation of the disc.

5.5.3 UsesThe prismatic compass is used for the following purposes:

(i) For preliminary survey of a road work.(ii) For rough traverses.

(iii) For the filling in of detail on topographical surveys.(iv) For military purposes, both for sketching and night marching.(v) For surveys in woody country.

5.5.4 LimitationsThe limitations of the prismatic compass are:

(i) Commonly used for rough surveys where speed, not accuracy, is themain consideration.

Optical and Surveying Instruments 189

(ii) Less accurate than a theodolite.(iii) The presence of iron or other magnetic substances near the station-

point may seriously affect the reading. If the bearing of each line isobserved twice, once at either end, any error due to local attraction canbe detected.

5.6 TheodoliteTheodolite is the most accurate instrument used in surveys for measuringhorizontal and vertical anlges. It is most useful to a surveyor for conductingprecise surveys. It has got two distinct motions for merasuring angles, one inthe horizontal plane which can be measured on a graduated horizontal circleby means of a Vernier, and the other in the vertical plane which can bemeasured on a graduated vertical circle by means of a Vernier.

5.6.1 Classifications of TheodolitesTheodolites may be classified as:

(i) Non-transit Theodolites In non-transit theodolites, the theodolite can-not be rotated on its horizontal axis to observe an angle. To observe theangle, its telescope is to be removed from its supports and turned from endto end.There are two types of non-transit theodolites:

(i) Wye or plain non-transit theodolite(ii) Everest non-transit theodolite.

These non-transit theodolites have become practically obsolete after theinvention of transit theodolites, only wye is sometimes used due to its com-pactness.

(ii) Transit Theodolites In transit theodolites, the telescope can be re-volved through a complete revolution about its horizontal axis. This theodo-lite is most commonly used. The types of transit theodolites are:

(i) Wild universal transit theodolites:(ii) Zeiss transit theodolite

(iii) American transit theodoliteTheodolites are also classified as Vernier and micrometer theodolites,

depending on whether Vernier or micrometer is used to read the angles.Sometimes, theodolites are differentiated according to the size of the di-

ameter of the graduated circle on the lower plate, which varies from 10 cm to25 cm. The smaller instruments are used for engineering work and survey,while the large ones are used for more precise (triangulation) work.

5.6.2 Parts of the TheodoliteThe essential parts of all classes of theodolites are the same. Figure 5.12show the sectional view of a transit theodolite (Vernier type), the main partsof which are described below:

(a) Telescope The telescope of the theodolite is of the terrestrial type,including a reticule. It is fitted with an object lens, eyepiece and a

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Sight

Bubble Tube for Settingof the Telescope

Vertical Circle

Telescope

Horizontal AxisAdjustmentDiaphragm Screw

Cover

Eyepiece A–frame

Vertical CircleTangent Screw

Vernier

Graduated arcLower Plate

Tangent Screw

Upper ParallelPlate

Levelling Screw

Lower ParallelPlate

Fig. 5.12 Transit Theodolite.

diaphragm, and is usually focussed by moving the object lens on rack andpinion. This method eliminates parallax error for close objects. Now-a-days,telescopes are the internal focussing type, and their eyepiece are screw-orspiral-focussing type, for easy and perfect adjustment. The reticule of thetelescope is mounted on a cell which is interchangeable with other tele-scopes.

The telescope is mounted on the horizontal axis, at right angles, and canbe rotated around it. The length of the telescope is limited by the height ofthe standard.

(b) The Standard Two uprights in the shape of the letter A are calledstandards, which stand up on the Vernier plate to support the horizontal axis.

Optical and Surveying Instruments 191

The telescope is supported by means of a transverse axis at right angles to itslength on this A frame.

(c) The Vertical Circle The vertical circle is rigidly attached to the tele-scope and moves with it. It is usually divided into four quadrants and thegraduations in each quadrant are numbered from 0° to 90°. In some instru-ments it is graduated continuously clockwise from 0° to 360°. By means ofthe vertical circle clamp and tangent screw, the telescope along with thevertical circle can be accurately set-up at any desired position in a verticalplane.

(d) The Horizontal Circle The horizontal circle consists of two parts, thecircle and the Vernier plate. The circle rotates inside the Vernier plate and isgraduated through 360° on the upper face, usually in 1/2° marks. The Ver-nier plate has a Vernier scale for reading angles on the circle. The Vernierusually has 30 divisions, reading to 1 of arc. The Vernier plate carries thepillars for the telescope and the compass box. Both table and plate rotate onconical bearings, and clamps and tangent screws are provided on both. TheVernier is usually read through a window in the plate assembly so that dustand moisture may be kept away from the scales and bearings.

Certain theodolites, known as direction instruments, are of extremely highprecision and are equipped with micrometers instead of Verniers. The hori-zontal circle is rotated by a worm-wheel mechanism instead of a tangentscrew.

(e) The Upper Plate or Circle The upper plate carries the standardswhich carry the telescope, and is capable of rotation about the vertical axis.

It is provided with Verniers (or vernier plates) which may be two or threein number.

(f) Lower Plate or Circle The outer axis is attached to the lower platehaving its edge bevelled. The edge (or limb) is silvered and graduated from0° to 360° in a clockwise direction into degrees and half-degrees, degreesand third of a degree, or degrees and sixths of a degree, depending upon thesize of the instrument. The diameter of the circle designates the size of theinstrument, e.g. 10 cm, 12 cm, 20 cm, etc. The lower plate is provided with aclamp-tangent screw by means of which it can be fixed accurately at anydesired position.

(g) Upper Clamp The upper clamp is used to fix the upper plate or circleto the lower plate or circle.

(h) Upper Tangent Screw The upper tangent screw is used to move theupper circle slowly over the lower circle, provided the upper clamp is fixed.The screw is protected from dust and wear by proper fittings.

(i) Lower Clamp The lower clamp is used to fix the lower plate or circleto the base of the instrument.

(j) Lower Tangent Screw The lower tangent screw is used to turn thelower circle round the vertical axis, provided the lower clamp is fixed.

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(k) Level Tubes On the surface of the vernier or upper plate, two leveltubes are fixed at right angles to each other. In addition, there is a long andsensitive bubble tube which governs the setting of the telescope for takingangles of elevation.

(l) Telescope Clamp It is used to fix the telescope to prevent it from anymovement in a vertical plane.

(m) Telescope Tangent Screw It is used to turn the telescope slowly ina vertical plane, provided the telescope clamp is fixed.

(n) Spindles or Axes There are two spindles or axes which are situatedone inside the other. The outer axis is hollow and its interior is groundconically to take the inner axis which is solid and conical. These two axeshave a common axis which forms the vertical axis of the instrument.

(o) Levelling Head It consists of two circular parallel plates, known asthe upper parallel plate and the lower parallel plate, which are connected bya ball and socket joint. The lower plate has an aperture in its centre throughwhich a plum bob may be suspended. The upper parallel plate is supportedby three or four levelling screws for levelling the instrument. The four-screwarrangement is not preferred because, due to uneven distribution of pressureon the screws, the wear of the screw is excessive. Generally, the three-screwarrangement is preferred as the instrument can be levelled more quickly andit is less liable to be damaged by over-strain. From the point of view ofstability also, three screws are as good as four screws.

(p) Index Bar (T-Frame) The index bar (or T-frame) is fixed in front ofthe vertical circle on the horizontal axis. It carries two Verniers on its twoarms. The vertical leg of the T-frame is known as the clipping arm and thetwo horizontal ends as index arms. The vertical leg is provided with a forkand two screws called the clip screws, at its lower end, to fix it to the bottomhorizontal member of the index bar.

A long sensitive bubble tube is attached either on top of the T-frame or onthe telescope.

(q) The Plum Bob To centre the instrument exactly over the station mark,a plum bob is suspended from the hook fitted to the bottom of the centralvertical axis.

(r) Tripod The theodolite is supported on a tripod when in use. It consistsof three legs which are fitted at their lower ends with pointed steel shoes inorder that they may be firmly pressed into the ground.

5.6.3 Some DefinitionsThe following terms should be well understood when using a transit theodo-lite:

(a) Centering Centering means the setting of the theodolite exactly overthe station mark, which is done with the help of a plum bob suspended froma small hook attached to the bottom of the vertical axis of the theodolite.

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(b) Transiting Transiting is the process of turning the telescope over thehorizontal axis, through 180° in the vertical plane, so that the eyepiece of thetelescope comes exactly in the opposite direction.

(c) Face Left Observation When the observations for vertical or hori-zontal angles are made through the telescope of a theodolite with the verticalgraduated circle on the left-hand side of the observer, it is known as face leftobservation.

(d) Face Right Observation It is an observation made with the verticalcircle on the right side of the observer.

(e) Changing Face It is the operation of bringing the vertical graduatedcircle of the theodolite from one side to the other.

(f) Back Sight It is usually the first sight taken after the transit is set-upover a station. It should preferably be a sight to the left-hand side station.

(g) Fore Sight The second and further sights taken while meausring hori-zontal angles are called fore sights.

5.6.4 Permanent Adjustments of TheodolitesFollowing are the permanent adjustments for a theodolite:

(i) The axis of the parallel plate levels must be perpendicular to the verti-cal axis.

(ii) The horizontal axis of the telescope must be at right angles (perpen-dicular) to the vertical axis.

(iii) The line of collimation must be at right angles to the horizontal axis.(iv) The axis of the altitude level (or the telescope level) must be parallel

to the line of collimation.(v) The vertical circle Vernier must read zero when the telescope level is

centered.

5.6.5 Precautions in the Use of TheodolitesThe following precautions must be taken while using a theodolite:

(i) After centering a theodolite, do not fix the locking nut of the head tootightly while using the shifting head.

(ii) Place the telescope vertical with the clamp slack and release the lowerclamp while carrying a theodolite.

(iii) The vertical arc should never be touched with the fingers as it willtarnish.

(iv) The telescope of the theodolite should be set vertically with the eye-piece down. In wet climate a waterproof hood should be used.

(v) When placing the transit in the box, special care should be taken sothat the telescope does not touch the sides of the box, and that allclamps are tightened so that the telescope cannot swing against thesides of the box during transport.

5.6.6 Applications of TheodolitesTheodolites are used for the following purposes in the field of surveying:

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(i) For the measurement of angles, e.g. horizontal angles, vertical angles,and deflection angles.

(ii) For the measurement of the magnetic bearing of a line.(iii) As a levelling instrument.(iv) As a tachometer.(v) To establish a line at a given angle with a line.(vi) To refer a point or line.

5.7 GyroscopeGyroscope is an instrument used for guiding airships and rockets in the rightdirection. It may be defined as a spinning wheel universally mounted so thatonly one point (its centre of gravity) is in a fixed poistion and the wheel isfree to turn in any direction around this point.

5.7.1 ConstructionA gyroscope, which is illustrated in Fig. 5.13, consists of a rotor and axlesupported by an inner ring with bearings on which the rotor and axle canrevolve. An outer ring with bearings is attached at 90° to the rotor bearing,about which the inner ring can revolve with its rotor and axle. The whole

Outer Ring

Spin Vector Inner Ring

Inner Pivot

Axle

Rotor (wheel)

BaseOuter Pivot

Fig. 5.13 Gyroscope

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arrangement is supported in a frame so that the rotor and its ring are sup-ported on horizontal bearings. The gyroscope asssembly can turn about avertical axis as well as a horizontal axis.

5.7.2 WorkingWhen the gyroscope is at rest, it is simply a wheel universally mounted andits axle can point in any direction without altering the geometrical centre ofthe whole assembly. But when the rotor is spun, the gyroscope exhibits twoimportant characteristics:

(i) It requires a high degree of rigidity and its axle keeps pointing in thesame direction, no matter how much the base is turned about. This isknown as gyroscope inertia.

(ii) The second characteristics is known as “precession” and may be illus-trated by applying a force to a gyroscope about the horizontal axis andthe vertical axis. When the force is applied about the horizontal axis,the applied force meets with resistance and that the gyroscope, insteadof turning about its horizontal axis, turns or ‘precesses’ about the verti-cal axis in the direction indicated by the arrow F in Fig. 5.14 (a).Similarly, when the force is applied about the vertical axis, the gyro-scope turns about its horizontal axis as shown by the arrow F, inFig. 5.14 (b).

Fig. 5.14 Principle of Gyroscope

Force

F

(a)

Force

F

(b)

5.7.3 ApplicationsAll practical applications of the gyroscope are based on the two characteris-tics discussed above. They are used to introduce desirable forces in (i) ships,(ii) aircrafts and (iii) monorail cars.

They are also used in instruments for maintaining directions, such as thegyrocompass.

SELF-CHECK QUIZ

A. Tick (ü) the appropriate answer:-1. A simple microscope is an instrument for viewing

(a) objects situated at large distances

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(b) close objects with two optical systems(c) close objects with a single optical system(d) none of these

2. The prismatic compass is an instrument for measuring(a) the foot of the perpendicular in survey work(b) rectangular offsets(c) angles in survey work(d) none of the above

3. Theodolite is used for(a) measuring horizontal and vertical angles(b) guiding airships and rockets(c) viewing an object at long distances(d) none of these

4. Gyroscope is an instrument used for-(a) levelling (b) measuring angles(c) measuring offsets (d) none of these

5. In refracting telescopes, the objective consists of(a) a paraboloidal mirror(b) a converging system of lenses of large focal lengths(c) a converging system of lenses of large focal lengths and large aperture(d) none of these

B. Fill-up the blanks:1. The resolution of a microscope is directly proportional to______ and inversely

proportional to ______.2. The minimum distance of comfortable vision in case of a microscope is ______.3. The stereoscopic microscope is essentially a ______ instrument.4. The optical square is an instrument used in ______ to find out ______.5. Gyroscope is used for ______, in the right direction.

C. State True/False:1. The value of the numerical aperture (NA) should not exceed 1.0 when the object

lies in a medium other than air.2. In a simple microscope, the lesser the focal length the greater is the magnification.3. In a compound microscope, the total magnification is obtained in two stages.4. A large magnification can be obtained from a simple microscope.5. The optical square belongs to a reflecting instrument which measures angles by

reflection.6. Prismatic compass is more accurate than the theodolite.

REVIEW QUESTIONS

1. What is the difference between a monocular and a binocular system? Describe, inbrief, the working of a level telescope or theodolite.

2. Explain with the help of sketches:(a) the working of a compound microscope,(b) the difference between a simple and a compound microscope. Explain the uses

of both.3. (a) Descrbe briefly the various types of compasses used in ships and aircraft.

(b) Write the principle of operation of Gyroscope.

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4. Write short notes on the following:(a) level indicators (b) prismatic compass(c) optical square (d) theodolite(e) gyroscope

5. What is a microscope? What are the different types of microscope? Explain any oneof them with a neat sketch.

6. What do you understand by the term resolution and magnification of the micro-scope?

7. Discuss the permanent adjustments done in theodolites, the precautions to be takenwhile using them and the applications of a theodolite.