Optical Square Model for School Maths Lab

Quick Answer: An Optical Square Model is a teaching model of the surveyor’s optical square, a small instrument in which two mirrors set at 45° to each other turn a line of sight through exactly 90°. Maths and surveying classes use the optical square model to set out perpendicular offsets from a survey line and to study the geometry of reflection.

How Two Mirrors Produce a Right Angle

A ray reflected by two plane mirrors in turn is deviated by twice the angle between the mirrors, whatever direction it arrives from. With the mirrors fixed at 45°, that deviation equals 90°. In the traditional instrument one mirror is only half silvered: the surveyor looks straight through the clear half at a ranging rod on the survey line and, at the same moment, sees in the silvered half an image of a second rod standing off to the side. When the two rods appear one above the other, the side rod is at right angles to the line.

That is why the instrument is used for offsets. Walking along a chain line with the optical square held to the eye, a surveyor finds the foot of the perpendicular from a tree, a building corner or a boundary stone, and the offset length is then measured with a tape. At school the same routine turns a playground into a geometry problem, letting a class set out a rectangle or a right triangle without a giant set square.

The listing names this item a model, so it is intended for teaching the principle rather than for field survey work; ask for the construction details if you need a particular form.

Specifications

Applications

• Setting out a perpendicular from a point on a survey line, and finding the foot of the perpendicular from an outside point
• Laying out a rectangular plot on the school ground and checking that its diagonals are equal
• Demonstrating the law of reflection and the double-reflection rule in a joint physics and maths lesson
• Comparing the optical method with the open cross staff and the 3-4-5 tape method for right angles

Care & Handling

• Keep the mirrors of the optical square model free of fingerprints and clean them with lens tissue or a soft cloth, never a rough towel.
• Before an outdoor lesson, set out one right angle and test it with a 3-4-5 triangle of tape; if the result is off, the mirror angle needs attention.
• Store the model in a padded box away from damp, which can tarnish mirror silvering.

Why Choose LabEquip

Schools that teach heights, distances and practical geometry outdoors tend to buy this model together with the Sextant Model, which works on the same double-reflection rule, and the Cross Vertical Staff Model, the non-optical way of setting right angles. All three are listed in the Mathematics School Lab Products range, and LabEquip can combine them in one order through the contact page.

Frequently Asked Questions

What is the difference between an optical square and a cross staff?

Both set out right angles in the field. A cross staff uses sighting slits or vanes cut at 90° and needs the user to line up two directions in turn. An optical square uses mirrors or a prism, so the survey line and the offset are seen together in one view, which makes it quicker to find the foot of a perpendicular while walking along the line.

Why do the mirrors have to be at 45 degrees?

After reflecting off two mirrors, a ray is turned through twice the angle between them. Half of 90° is 45°, so that setting gives a right angle. If the mirrors were set at 30°, the instrument would turn the sight line through 60° instead.

Can an optical square find the foot of a perpendicular from a tree?

Yes, that is its most common use. Walk along the survey line looking through the instrument until the image of the tree lines up with the ranging rod ahead. The spot where you stand is the foot of the perpendicular, and the tape distance from there to the tree gives the offset.

How can students check that the model gives a true right angle?

Set out a right angle with it, then measure 3 m along one arm and 4 m along the other with a tape. If the gap between those two points measures 5 m, the angle is 90°, because 3, 4 and 5 satisfy the Pythagorean relation.

Is an optical square the same as a prism square?

They do the same job. A prism square replaces the two mirrors with a pentagonal prism, which keeps its 90° deviation without adjustment. The mirror version is easier to explain in class because students can see both mirrors and trace the path of the light.

Which lessons use an optical square model?

It fits lessons on perpendicular lines and offsets, practical geometry on the school ground, and the reflection of light in physics. Vocational surveying courses also use it to introduce chain surveying.

Last Updated: September 2026