Tacheometry by optical wedge (subtense wedge) system: The theodolites designed for this method have which distinctive feature?

Introduction / Context:
Tacheometric distance measurement can be achieved by several optical principles: fixed stadia hairs, anallatic lenses, and optical wedge (subtense wedge) systems. The wedge method introduces a fixed angular separation in the line of sight, allowing distance to be computed from the staff intercept formed by the wedge, without relying on traditional stadia hairs.

Given Data / Assumptions:

• Instrument is a theodolite adapted for tacheometry.
• Optical wedge produces a constant small angular displacement.
• Standard staff with suitable markings is observed.

Concept / Approach:

In the optical wedge system, a glass wedge (or a pair forming a small prism angle) is fitted inside the telescope. The wedge splits or displaces the image to create a fixed angular subtense at the eye. The observed intercept on the staff, when multiplied by a constant, yields the horizontal distance. This differs from classical stadia where stadia hairs define the fixed subtense.

Step-by-Step Solution:

Verification / Alternative check:

Manufacturer specifications of wedge tacheometers describe an internal optical wedge element and corresponding constants, confirming option (c).

Why Other Options Are Wrong:

(a) describes stadia-hair tacheometers; (d) implies an external wedge in front of the objective, uncommon in standard designs; (e) refers to a different micrometer-based technique; (b) is incomplete because although classical stadia hairs may be omitted, the defining feature is the internal wedge.

Common Pitfalls:

Confusing an anallatic lens (which corrects additive constant) with a wedge system; assuming the wedge is external rather than internal.

Final Answer:

A glass wedge fitted inside the telescope