Autocollimator is an optical instrument used to measure small angular displacements with high accuracy. It is commonly used in mechanical engineering and metrology applications. The correct answer to the given question is option 'C', which states that an autocollimator is used to measure small angular displacement on a flat surface.

Below, I will explain in detail how an autocollimator functions and why it is used for measuring angular displacements:

1. What is an Autocollimator?
An autocollimator consists of a collimator, a telescope, and a light source. The collimator projects a parallel beam of light onto a target mirror or surface. The reflected light returns through the telescope to the observer. The telescope forms an image of the reflected light, which can be observed and measured.

2. Principle of Operation:
The principle of operation of an autocollimator is based on the measurement of the deviation of the reflected light beam. When the target mirror or surface is perfectly aligned with the autocollimator, the reflected light beam returns along the same path as the incident beam. However, when there is an angular displacement, the reflected beam deviates from the incident beam.

3. Measurement of Angular Displacement:
By observing the deviation of the reflected beam, the angular displacement of the target mirror or surface can be determined. The autocollimator is equipped with a scale or a reticle in the eyepiece, which allows the observer to measure the angular deviation accurately. The scale can be calibrated to provide direct readings of the angular displacement.

4. Applications:
Autocollimators are widely used in various applications where precise measurement of angular displacements is required. Some common applications include:
- Alignment of optical elements: Autocollimators are used to align mirrors, lenses, and other optical components in optical systems.
- Measurement of straightness and flatness: By measuring the angular deviation of a surface, the flatness or straightness error can be determined.
- Measurement of angular errors in machinery: Autocollimators are used to measure and align rotational axes, checking for any angular misalignment or errors.
- Surface inspection: Autocollimators can be used to detect surface defects or irregularities by measuring the angular deviation of the reflected beam.

In conclusion, an autocollimator is an optical instrument used to measure small angular displacements on a flat surface. It is widely used in mechanical engineering and metrology applications for precise alignment and measurement of angular errors.