The spherometer is a measuring instrument used in the machining of an astronomical mirror, to verify the depth of the sagitta, and then the radius of curvature of the surface under examination.

The instrument itself is not complicated, It's consists of a rigid supporting structure on which are placed 3 support feet arranged so as to be located at the vertices of an equilateral triangle, and in the center is positioned a screw device or a dial indicator to measure the depth of the excavation.

Knowing the radial distance of the legs from the Central rod and depth measured, You can, by means of appropriate mathematical formulas, go up to the value of the radius of curvature of the surface.

Mobile measuring rod, If screw type system, is generally fromed by a screw whit lead equal to 1 mm integral with a graduated disk with 100 divisions, which then allows a reading of the measure of the order of hundredths of a millimeter.

The three legs instead, can be formed by sharp rods, or three spheres of known diameter. The main difference between the two solutions are in the different formulas that you must use to calculate the final result.

In particular the formulas to be used are:

being:

**R** = radius of curvature of the surface (2 times the focal length)

**h** = measured value of the sagitta

**r** = radial distance from the central srew-legs

**d** = diameter of spheres used

± Present in the formula for the calculation of the radius of curvature for the spherometer with spheres should be understood as a sign + if it is analyzing a concave surface, While as a sign – if it is analyzing a convex surface.

Another variation of the instrument is shown below, where in place of the three supports is a cylindrical tubular section. In this variant, if you analyze a concave surface to rest on it will be the outer circular ring, while if one analyzes a convex surface to rest on it will be the inner ring. It will be important to use the correct value of the RADIUS (r) in the formula, Depending on the case.

**HOW TO USE IT**

- The first operation to perform is to verify the zeroing of the instrument going to making a measurement on a flat surface.

- Proceed with the measuring surface to be analyzed.

If you have a spherometer dial indicator measurement will take place immediately and and without fatigue, while if you have one of srew spherometer, you should turn the screw to get it down until its tip comes in contact with the surface.

Techniques to understand when contact occurred are mainly 2:

In the first, Once you get in contact and you continue to turn the screw, the entire spherometer will tend to turn on itself, then return back slightly until it reaches the ideal location (sensitivity 3-5 hundredths of mm); in the second, if also just slightly exceeds,, the value of the sagitta, one of the legs will detach from the surface of the glass. If pressure is applied alternately over the feet you should hear a clicking sound (as with a wobbly table), then go back up to the disappearance of the effect (sensitivity 1-2 hundredths of mm).

- Now read the measurement and using the correct formula to calculate the radius of curvature of the surface (or the focal length by dividing by 2 the result).

The following example sets the value of the arrow is just over 0.81 mm (being the concave surface of the dipstick is decreased with respect to the zero position, then the pointer is moved in a counterclockwise direction).

By applying the above formula, the result of the radius of curvature (R) amounted to 920.6 mm (having the spherometer concerned r = 39 mm and d = 7.95 mm).

**EXAMPLE OF A SPHEROMETER HOMEBUILT:**

For the construction of this spherometer I used as a base of support in a fairly sturdy plastic gear and of appropriate diameter recovered from an old copier..

I have used this support because as you can see from the image below has a circular area on the outside of delimited by two edges that allow me to position accurately (at least radial level) the three spheres of steel support. it is 12 radial ribs that allow me to place the spheres at 120° to each other.

To lock in position the comparator instead, it's drill a hole of adequate size to allow passage of the outer Rod cursor that has been clamped into place by a transversal screw.

And this is the spherometer full placed on a flat surface for zeroing:

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