Optical square principle in chain surveying The construction of an optical square, used to set out right angles for offsets, is based primarily on which optical principle?

Introduction / Context:
The optical square is a compact instrument that enables the surveyor to lay off a precise 90° angle when setting offsets from a chain line to details. Its design cleverly uses mirror geometry to obtain an exact right angle without the bulk of a full theodolite or prism pole.

Given Data / Assumptions:

• The instrument uses two mirrors (one half-silvered) inclined at 45°.
• Incident and reflected rays obey the law of reflection.
• The desired included angle between the two lines of sight is 90°.

Concept / Approach:

By arranging two planar mirrors to produce two successive reflections, the outgoing ray is rotated by twice the angle between the mirrors. Setting the mirrors at 45° therefore yields a net deflection of 90°. This is the essence of the optical square—achieving a right angle through double reflection. Refraction or double refraction are not involved; there is no prism bending of light as in a prismatic compass.

Step-by-Step Solution:

Verification / Alternative check:

Field practice confirms that aligning the direct and reflected images of the ranging rod indicates the rod is set at right angles to the chain line.

Why Other Options Are Wrong:

Single reflection yields 2*mirror-tilt only once; refraction/double refraction are prism phenomena; diffraction is irrelevant.

Common Pitfalls:

Confusing optical square with prism square (which uses refraction); misadjusted mirrors causing small angular errors.

Final Answer:

double reflection