Understanding the Optical Square in Surveying

An optical square is a compact surveying instrument used primarily for setting out lines at right angles (90°) to a main survey line, also known as a chain line or baseline. This is a fundamental task in surveying for establishing boundaries, plotting features, and laying out construction.

Components of an Optical Square: Horizon and Index Glasses

The optical square uses mirrors (or sometimes prisms) to achieve the 90° offset. The key components are:

• Horizon Glass: This glass is typically half-silvered. It allows the surveyor to see directly through the unsilvered part along the main survey line towards a distant point or flag. The silvered part reflects light from the index glass towards the eye.
• Index Glass: This glass is fully silvered. It receives light from the point intended to be at a right angle to the main survey line and reflects it towards the horizon glass.

Both glasses are housed within a frame with slits for sighting.

Angles of the Glasses relative to the Sight Lines

The functionality of the optical square depends on the precise angles at which the horizon glass and index glass are set relative to the main line of sight (the horizon sight). According to standard construction, these angles are fixed:

• The horizon glass is placed at an angle of 120° with the horizon sight.
• The index glass is placed at an angle of 105° with the index sight (which is along the same main line of sight).

These specific angles ensure that light reflecting off the index glass and then the silvered part of the horizon glass comes from a point located exactly at a 90° angle to the direct sight line.

How an Optical Square Works: The Principle of Double Reflection

The operation of the optical square is based on the optical principle of double reflection. When a ray of light is reflected successively by two plane mirrors, the angle of deviation (the angle between the initial ray and the final ray) is twice the angle between the two mirrors.

To set out a right angle (90°), the optical square needs to deviate the light ray from the object at the right angle by 90° so that it appears to coincide with the direct line of sight. According to the double reflection principle, to achieve a 90° deviation, the angle between the reflecting surfaces of the index glass and the horizon glass must be:

\($$ \text{Angle between mirrors} = \frac{\text{Angle of deviation}}{2} = \frac{90^\circ}{2} = 45^\circ $$\)

The manufacturing setup where the horizon glass is at 120° and the index glass is at 105° relative to the main sight line achieves this required 45° angle between the reflecting surfaces of the mirrors, allowing the instrument to accurately set out perpendicular lines.

When using the optical square, the surveyor looks through the horizon glass. They can simultaneously see the target along the main survey line directly and the image of an object (like a ranging rod) placed roughly perpendicular to the line, reflected via the index glass and the horizon glass. By moving the object perpendicular to the line, its reflected image is brought into coincidence with the direct view of the survey line target. When they coincide, the object is exactly at a right angle to the survey line.

Key Angles Summary

Setting Out Right Angles in Surveying

The ability of the optical square to quickly and accurately set out 90° angles makes it a valuable tool for various surveying tasks, including:

• Laying out boundaries.
• Establishing perpendicular offsets to locate features.
• Setting out corners for structures.

Revision Table: Optical Square Angles

Additional Information on Surveying Instruments for Right Angles

While the optical square is a common method for setting out right angles, other instruments can also be used:

• Cross Staff: A simpler, older instrument that uses slits or mirrors to sight along the main line and at a 90° angle. It is less precise than an optical square.
• Prism Square: Similar in principle to the optical square, but uses prisms instead of mirrors. Prisms are less prone to getting out of adjustment than mirrors. They also work based on the principle of light deviation to achieve the 90° angle.
• Theodolite or Total Station: Modern electronic instruments that can measure and lay out angles (including 90°) with very high precision.
• Pythagorean Theorem (3-4-5 rule): A simple method using a measuring tape to form a right-angled triangle with sides in the ratio 3:4:5 (or any multiple thereof) to establish a perpendicular line.

Each instrument has its advantages and disadvantages in terms of accuracy, cost, and ease of use in different field conditions.