---
title: "Face observation errors; optical theodolite"
subject: "Surveying I"
chapter: 7
key: "semester_3/surveying_i:face-observation-errors-optical-theodolite"
source: https://www.bctengineer.com/q/semester_3/surveying_i/face-observation-errors-optical-theodolite
site: BCT Engineering
---

# Face observation errors; optical theodolite

Surveying I · Chapter 7: Transit and Theodolite

- Asked in: 2080 Baisakh, 2+2 marks; 2076 Chaitra, 2+2 marks (asked 2 times)
- Video: [Part 9 ! Theodolite ! Left face ! Right face ! Face change ! Theodolite lecture ! Survey lecture](https://www.youtube.com/watch?v=acALScL-PHo) — NARAYANA COACHING CLASSES
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/face-observation-errors-optical-theodolite
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-7

## Question

List out the errors which are eliminated by taking face observations of the theodolite; also explain the mechanism of elimination with neat sketches. Explain the principles of operation of an optical (micrometer) theodolite.

## Short answer

Face observations eliminate collimation error, horizontal axis inclination error, vertical circle index error, and eccentricity. Reversing the face causes errors to reverse sign, so the mean of face left and face right cancels them. In optical theodolites, glass circles are read through a microscope; a micrometer screw turns a plane-parallel plate to shift the graduation image, giving direct readings to seconds.

## Answer

#### Errors eliminated by face observations
**Face observation** means observing a point with the telescope in the face-left position (vertical circle on the left, FL), then again after transiting the telescope and turning the instrument through 180 degrees (face right, FR), and taking the mean.

| Error | Cause |
|---|---|
| Line of collimation error | Line of sight not perpendicular to the horizontal axis |
| Horizontal (trunnion) axis error | Horizontal axis not perpendicular to the vertical axis |
| Vertical circle index error | Vernier zero not exactly at the zero of the vertical circle when the telescope is horizontal |
| Eccentricity of the vertical circle / vernier (partly) | Centre of the circle not on the axis |
| Error due to the line of collimation and altitude bubble not being parallel | Altitude bubble axis not parallel to the line of sight |

#### Mechanism of elimination
**1. Collimation error.** On face left the line of sight deviates from the correct direction by a small angle $e$ to one side. After changing face, the deviation is on the *opposite* side, so one reading is too large by $e$ and the other is too small by $e$. The mean is free of the error.

```text
  FL:   X-------- true line ---------> P
          \_ line of sight (+e)
  FR:   X-------- true line ---------> P
          /_ line of sight (-e)
        mean of FL and FR = true direction
```

**2. Trunnion axis error.** If one end of the horizontal axis is higher, the telescope sweeps an inclined plane. After changing face, the high end is on the opposite side, so the angular error changes sign and cancels in the mean. (The error is large only for steep sights.)

**3. Index error of the vertical circle.** If the vertical circle reads $+i$ on face left when the line of sight is horizontal, the same error has the opposite effect on face right. The mean of the two vertical angles is free of $i$.

For horizontal angles, both verniers (A and B, 180 degrees apart) are also read and averaged, which removes the error due to **eccentricity of the centre of the circle**.

#### Principle of operation of an optical (micrometer) theodolite
In an optical theodolite the horizontal and vertical circles are made of glass and are finely graduated (for example, at 20 minute intervals). The images of the graduations are carried by a system of prisms and lenses to a reading microscope placed beside the eyepiece of the telescope. The observer reads the angle through this microscope without moving from the observing position.

- The circle is lit by a mirror (or a lamp), and the light passes through the circle, a prism system and a lens to the reading eyepiece.
- In a **micrometer** theodolite, the graduations of diametrically opposite sides of the circle are brought into the same field of view, so the reading is automatically the mean of the two sides. This removes the error of eccentricity.
- A **micrometer screw** turns a plane-parallel glass plate in the optical path. Turning it shifts the image of the circle graduations until the index line coincides exactly with a main graduation line. The drum attached to the screw is graduated in minutes and seconds and gives the fraction of the smallest circle division.

```text
   mirror -> circle -> prisms
        -> micrometer plate -> eyepiece
      (plate turned by micrometer screw)

   reading = circle division + micrometer drum reading
```

Its advantages are: no verniers, quick and accurate reading to 1 second or even 0.1 second, a lighter and sealed instrument, and elimination of the eccentricity error.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Why does taking both faces eliminate collimation error?
   A. The error is the same on both faces and is added
   B. The bubble is re-centred
   C. The deviation is on opposite sides, so one reading is too large and the other too small by e
   D. The verniers are averaged
   Answer: C. The mean of the two faces is free of the error. (Key point: Collimation error)

2. How is vertical circle index error removed?
   A. By averaging two verniers
   B. By parallax removal
   C. By levelling
   D. By the mean of the vertical angles on both faces
   Answer: D. The error has opposite effect on the two faces. (Key point: Index error)

3. How is eccentricity of the circle removed?
   A. By reading both verniers (180 degrees apart) and averaging
   B. By changing face only
   C. By focusing
   D. By clamping
   Answer: A. Diametrically opposite readings cancel eccentricity. (Key point: Eccentricity)

4. What does the micrometer screw do?
   A. Levels the instrument
   B. Turns a plane-parallel plate to shift the graduation image until it coincides with the index
   C. Focuses the eyepiece
   D. Rotates the vertical axis
   Answer: B. The drum then gives the fraction of the smallest division. (Key point: Micrometer screw)

## Related in Surveying I

- [Errors eliminated by face observation](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aface-observation-errors-and-temporary-adjustment) — Surveying I, chapter 7
- [Theodolite construction principle; micrometer](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atheodolite-construction-principle-micrometer) — Surveying I, chapter 7, asked 2×
- [EDM operation principles and errors](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aedm-operation-and-errors) — Surveying I, chapter 2, asked 2×
- [Plotting theodolite traverse; repetition errors](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aplotting-theodolite-traverse-repetition-errors) — Surveying I, chapter 7