An optical square is based on which of the following principles?

🔊 Understanding the Optical Square

The optical square is a simple, hand-held instrument used by surveyors to accurately set out right angles (90°) on the field. Its operation is based entirely on a precise law of optics involving mirrors, which allows it to be both accurate and easy to use for tasks like setting out offsets from a chain line.

🔬 Detailed Analysis: The Principle of Double Reflection

The core principle behind the optical square is the law of reflection applied twice. This law states that the angle between the first incident ray and the final reflected ray is twice the angle between the two mirrors.

In an optical square, two mirrors—the index glass and the horizon glass—are fixed at a precise angle to each other.

• The angle between the mirrors is intentionally set to 45°.
• Therefore, the angle of deviation of the light ray after reflecting off both mirrors is 2 x 45° = 90°.

This fixed 90° deviation is what allows the instrument to establish a perfect right angle from the line of sight.

🔧 Construction and Key Angles

The instrument is cleverly designed to achieve this principle with just two key components inside a small, protected casing:

• Index Glass (I): This mirror is fully silvered and reflects the light coming from the object being sighted (e.g., a ranging rod).
• Horizon Glass (H): This mirror is half-silvered and half-plain. The surveyor looks through the plain (unsilvered) half to see the forward station, while the silvered half receives the reflection from the index glass.
• The crucial angle between the Index Glass (I) and the Horizon Glass (H) is fixed at exactly 45°.

💡 Study Tips

• Primary Use: Setting out right angles (90°).
• Governing Principle: Double reflection.
• Mirror Angle: The two mirrors are fixed at an angle of 45° to each other.
• Resulting Angle: The deviation between the original line of sight and the final reflected image is always 90° (2 x 45°).