---
title: "Principle of optical distance measurement"
subject: "Surveying II"
chapter: 2
key: "semester_4/surveying_ii:optical-distance-measurement-principle"
source: https://www.bctengineer.com/q/semester_4/surveying_ii/optical-distance-measurement-principle
site: BCT Engineering
---

# Principle of optical distance measurement

Surveying II · Chapter 2: Tacheometry

- Asked in: 2077 Chaitra, 3 marks
- Video: [Principle of Tacheometry - Civiconcepts](https://www.youtube.com/watch?v=V77Pf2-5_iw) — Civiconcepts - Bhushan Mahajan
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/surveying_ii/optical-distance-measurement-principle
- Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-2

## Question

Explain the principle of optical distance measurement.

## Short answer

Optical distance measurement finds distance from a small parallactic angle β subtended by a known base s, or from a known angle and staff intercept. For subtense, D=(s/2)cot(β/2); for stadia with fixed angle, D=Ks+C; for tangential, D=s/(tanθ1−tanθ2).

## Answer

**Principle:** in optical distance measurement the distance to a point is found from the instrument alone, by measuring a small angle subtended at the instrument by a known length (or a length subtended by a known angle), instead of taping the distance. It rests on the geometry of a thin isosceles triangle:

$$
D=\frac{s}{2}\cot\frac{\beta}{2}\approx\frac{s}{\beta}
$$

where $s$ is the base (known length) and $\beta$ the parallactic angle at the instrument.

```text
 Instrument                       Staff / bar
     O  <-------------- D -------------->  A
      \  beta                              | s
       \_________________________________  B
```
Depending on which quantity is fixed:
1. **Stadia method:** the angle $\beta$ is fixed by two stadia hairs in the telescope, and the intercept $s$ on the staff varies. $D=Ks+C$.
2. **Subtense method:** the length $s$ is fixed (a subtense bar, 2 m long) and the angle $\beta$ is measured by the theodolite. $D=\frac{s}{2}\cot\frac{\beta}{2}$.
3. **Tangential method:** the vertical angles to two targets a known distance apart on a staff are measured. $D=s/(\tan\theta_1-\tan\theta_2)$.

The horizontal distance and the difference in elevation are then obtained from the distance and the vertical angle, so that detail surveys and contouring can be done faster than by chaining, especially in rough ground.

## Check yourself

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

1. What is the principle of optical distance measurement?
   A. Time of flight of a light pulse
   B. A small angle subtended by a known length, giving D = (s/2) cot(beta/2) approx s/beta
   C. Counting tape lengths
   D. Phase shift of a modulated wave
   Answer: B. Distance follows from the thin isosceles triangle formed by a known base and the parallactic angle. (Key point: Core principle)

2. In the stadia method, which quantity is fixed?
   A. The staff intercept s
   B. The angle beta between stadia hairs
   C. The distance D
   D. The vertical angle
   Answer: B. The stadia hairs fix beta; the intercept s varies and D = Ks + C. (Key point: Stadia method)

3. In the subtense method, which is fixed and which is measured?
   A. Angle fixed, length measured
   B. Length fixed (2 m bar), angle measured
   C. Both fixed
   D. Both measured with a tape
   Answer: B. The bar length is fixed and the horizontal angle is measured by theodolite. (Key point: Subtense method)

4. The tangential method gives D as
   A. Ks + C
   B. s/(tan theta1 - tan theta2)
   C. (s/2) cot(beta/2)
   D. s cos theta
   Answer: B. Vertical angles to two targets s apart give D = s/(tan theta1 - tan theta2). (Key point: Tangential method)

## Related in Surveying II

- [Optical distance principle, tangential horizontal distance](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aoptical-principle-tangential-horizontal-distance) — Surveying II, chapter 2
- [Tacheometry principle, stadia distance and RL](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atacheometry-principle-stadia-formula) — Surveying II, chapter 2
- [ODM principle, tacheometric field procedure](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aodm-principle-field-procedure-theodolite) — Surveying II, chapter 2
- [Stadia principle, tangential method depression](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Astadia-principle-tangential-depression) — Surveying II, chapter 2

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