---
title: "Autocollimator and angle dekkor"
subject: "Metrology"
chapter: 5
key: "semester_3/metrology:autocollimator-and-angle-dekkor"
source: https://www.bctengineer.com/q/semester_3/metrology/autocollimator-and-angle-dekkor
site: BCT Engineering
---

# Autocollimator and angle dekkor

Metrology · Chapter 5: Angular and Taper Measurement

- Asked in: year not given, 8 marks
- Video: [Lecture 12 - Autocollimator- Principle and Working](https://www.youtube.com/watch?v=6BfT7rhWQtM) — Fundamentals of Engineering
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/metrology/autocollimator-and-angle-dekkor
- Whole chapter: https://www.bctengineer.com/md/semester_3/metrology/chapter-5

## Question

Explain with neat sketches the principle and working of an autocollimator. Describe the angle dekkor and state where each is used.

## Short answer

Autocollimator measures small tilts by shift x=2θf of reflected image. Angle dekkor uses a fixed scale and graticule to read tilt directly up to ±1° (LC 1 min). Autocollimator used for straightness, flatness; dekkor for angle gauges and tapers.

## Answer

#### Autocollimator
An autocollimator is an optical instrument that measures very small angular tilts (down to 0.1 s) of a reflecting surface at a distance. It combines a collimator and a telescope.

**Principle:** A target (cross-wire) at the focus of an objective lens gives a parallel beam. If the beam strikes a plane mirror exactly normal to it, the beam returns on itself and the reflected image falls on the target. If the mirror tilts by an angle $\theta$, the reflected beam turns by $2\theta$ and the image shifts by

$$
x = 2\,\theta\, f
$$

where $f$ is the focal length of the objective.

```text
 lamp--> [cross-wire] --|beam splitter|--> objective --->| mirror
                               |            (f)  parallel |
                           eyepiece  <---- reflected beam-|
                           micrometer
```
Light from the lamp illuminates the target, passes through the beam splitter and objective, goes to the mirror, returns and forms an image of the target in the eyepiece. The shift is read by a micrometer eyepiece graduated in seconds of arc.

**Uses:** checking straightness and flatness of machine beds and surface plates, squareness, parallelism of slideways, angle of prisms and polygons, and calibration of angle gauges and indexing tables. The mirror is fixed on a carriage moved along the bed.

#### Angle dekkor
It is also an autocollimator but with a fixed illuminated scale and a fixed graticule with a cross-line in the eyepiece. The reflected image of the scale is seen superposed on the fixed graticule, and the reading gives the tilt directly in minutes. Angle dekkor measures angles up to about $\pm 1^\circ$ with a least count of 1 minute (and 0.5 min estimated).

For measuring an angle of a component, slip gauges and a sine bar are used to set the working face to a known angle, and the dekkor reading shows the difference from the nominal angle (e.g. checking angle gauges, taper plugs, and bevel angles).

| | Autocollimator | Angle dekkor |
|---|---|---|
| Target | Cross-wire | Scale and fixed graticule |
| Range | Very small angles | Up to about $\pm 1^\circ$ |
| Accuracy | 0.1 to 1 s | About 1 minute |

## Check yourself

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

1. If the mirror in front of an autocollimator tilts by theta, the reflected beam turns by:
   A. theta/2
   B. theta
   C. 2 theta
   D. 4 theta
   Answer: C. A reflected ray turns through twice the mirror tilt, so the image shift is x = 2 theta f. (Key point: Autocollimator principle)

2. The image shift in an autocollimator is given by:
   A. x = theta f
   B. x = 2 theta f
   C. x = theta/f
   D. x = 2 theta/f
   Answer: B. x = 2 theta f, where f is the focal length of the objective. (Key point: Image shift)

3. Which is a typical use of an autocollimator?
   A. Measuring bore diameter directly
   B. Checking straightness and flatness of machine beds and surface plates
   C. Measuring surface roughness
   D. Measuring mass
   Answer: B. Autocollimators check straightness, flatness, squareness, parallelism of slideways and angles of prisms and indexing tables. (Key point: Autocollimator uses)

4. How does the angle dekkor differ from a simple autocollimator?
   A. It uses a fixed illuminated scale and fixed graticule, reading tilt directly in minutes over about ±1°
   B. It uses a cross-wire and reads seconds only
   C. It measures only linear distance
   D. It needs no light source
   Answer: A. The dekkor superposes an illuminated scale image on a fixed graticule, with least count about 1 minute and range about ±1°. (Key point: Angle dekkor difference)

## Related in Metrology

- [Sine bar principle, setting and error](https://www.bctengineer.com/question.md?key=semester_3%2Fmetrology%3Asine-bar-setting-and-error) — Metrology, chapter 5

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