Optical square – fixed angle between the two mirrors In an optical square used for setting out right angles, the acute angle between the two mirrors is equal to which value?
Correct Answer: 45°
Introduction / Context:An optical square is a simple reflective instrument widely used in chain surveying to set out perpendiculars (right angles). It consists of two mirrors oriented at a specific acute angle so that due to reflection geometry, the user can align one sight along the chain line and set a perpendicular to it. This question asks for the fixed angle between the mirrors that yields a 90° observation.
Given Data / Assumptions:
- The device uses the law of reflection: angle of incidence equals angle of reflection.
- Two-mirror reflection rotates a ray by twice the angle between the mirrors.
- We desire a right-angle deflection between the two observed directions.
Concept / Approach:
If the angle between mirrors is α, a ray incident on the first mirror and then reflected by the second is deflected by 2α. To set out a right angle (90°), we require 2α = 90°, hence α = 45°. Optical squares are therefore manufactured with mirrors inclined at 45°, producing a perceived perpendicular when the reflected and direct images coincide correctly.
Step-by-Step Solution:
1) Desired deflection between chain line and offset = 90°.2) Two reflections → net deflection = 2α.3) Set 2α = 90° → α = 45°.4) Therefore mirror angle = 45°.Verification / Alternative check:
Instrument descriptions of optical squares and prism squares align with this 45° mirror setting to achieve perpendicular offsets without a theodolite.
Why Other Options Are Wrong:
20°, 30°, 60°: Would produce 40°, 60°, or 120° deflections, not a right angle.
90°: Would lead to 180° deflection, not usable for perpendicular offsets.
Common Pitfalls:
Confusing the acute mirror angle with the desired right angle; mixing prism square (which uses refraction) with the mirror-based optical square.
Final Answer:
45°