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Which of the following instruments are used for setting out right angles?
Cross staff
Optical square
Prism square
All of the above
All of the above
Instruments used for setting out right angles are known as optical or physical offsets tools in chain surveying. Cross staffs, optical squares, and prism squares all operate on specific geometric principles to establish perpendicular lines (90° offsets) from a survey line.
Instruments used for setting out right angles are known as optical or physical offsets tools in chain surveying. Cross staffs, optical squares, and prism squares all operate on specific geometric principles to establish perpendicular lines (90° offsets) from a survey line.
δ=2α — deviation principle for optical square where α is the angle between mirrors.
θ=90° — standard right angle offset.
The Cross Staff relies on visual alignment of perpendicular slits. The Optical Square uses the principle of double reflection: a light ray reflected twice from two mirrors at an angle of 45° results in a deviation of 90°. The Prism Square uses a pentaprism to deviate a light ray by exactly 90° through internal reflection, requiring no adjustment.
Cross staff: Simplest, least accurate, based on simple sighting through slits.
Optical square: More accurate, based on the principle of double reflection (45° mirror orientation).
Prism square: Most compact and maintenance-free, utilizes a pentaprism.
All these instruments are used for laying out offsets perpendicular to the chain line.
Increases speed of field work.
Ensures accuracy in marking ground features.
Prism squares do not require periodic adjustments like optical squares.
Cross staffs are affected by parallax error.
Optical squares are sensitive to mirror misalignment.
Requires clear visibility between stations.
Laying out buildings and structures.
Defining boundaries for cadastral surveying.
Offset measurements in chain surveying.
| Feature | Optical Square | Prism Square |
|---|---|---|
Working Basis | Optical Reflection (2 mirrors) | Internal Prism Reflection |
The optical square is based on the laws of reflection: the angle of incidence equals the angle of reflection.
An open cross staff is the most basic form, essentially a hollow square or octagon with vertical slits.
D is correct — Cross staffs, optical squares, and prism squares are all standard field instruments used in chain surveying to set out perpendicular lines.
Always remember that while all these instruments provide 90° offsets, the 'prism square' is preferred in modern practice due to its ruggedness and lack of adjustment requirements.