Spherometer
Encyclopedia
A spherometer is an instrument for the precise measurement of the radius
of a sphere
. Originally, these instruments were primarily used by optician
s to measure the curvature
of the surface of a lens
.
The usual form consists of a fine screw moving in a nut carried on the centre of a small three-legged table or frame; the feet forming the vertices of an equilateral triangle. The lower end of the screw and those of the table legs are finely tapered and terminate in hemispheres, so that each rests on a point. If the screw has two turns of the thread to the millimetre the head is usually divided into 50 equal parts, so that differences of 0.01 millimetre may be measured without using a vernier
. A lens, however, may be fitted, in order to magnify the scale divisions. A vertical scale fastened to the table indicates the number of whole turns of the screw and serves as an index for reading the divisions on the head.
A contact-lever, delicate level or electric contact arrangement may be attached to the spherometer in order to indicate the moment of touching more precisely than is possible by the sense of touch. To measure the radius of a sphere—e.g. the curvature of a lens
—the spherometer is levelled and read, then placed on the sphere, adjusted until the four points exert equal pressure, and read again. The difference gives the thickness of that portion of the sphere cut off by a plane passing through the three feet.
Calling this distance h, and the distance between the feet a, the radius R is given by the formula:
, it can be employed for other purposes than measuring the curvature of a spherical surface. For example, it can be used to measure the thickness of a thin plate.
To do so, the instrument is placed on a perfectly level plane surface and the screw turned until the point just touches; the exact instant when it does so is defined by a sudden diminution of resistance succeeded by a considerable increase. The divided head and scale are read; the screw is raised; the thin plate slipped under it; and the process is repeated. The difference between the two readings gives the required thickness.
Similarly, the instrument can measure the depression in an otherwise flat plate. The method would be as for measuring the thickness of a plate, except that the micrometer portion is placed over the depression and the measurement is taken below the surface instead of above.
This type of instrument is commonly seen used in inspections of oil field tool pipe for metal surface pits, fractures, and roundness before being shipped to drilling sites for exploratory wells. See drill pipe
. The process of inspections are designed to remove weakened tool pipe, so that pipe will not fracture during drilling. Tool pipe with thicker than 1" walls for a 4" diameter tube of hardened steel, fitted with tapered thread collars are re-used after drilling is complete, and thinner-walled tubular oil-well casing is in place. Electronic instrumentation similar to the spherometer in design are modified at inspection plants for casing, tubing, and drill pipe. The equivalent measurements in optics would be for a cylinder, or lens with a cylindrical component having an optical axis, where a plane through the lens would produce an oval circumference.
Radius
In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter. If the object does not have an obvious center, the term may refer to its...
of a sphere
Sphere
A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...
. Originally, these instruments were primarily used by optician
Optician
An optician is a person who is trained to fill prescriptions for eye correction in the field of medicine, also known as a dispensing optician or optician, dispensing...
s to measure the curvature
Curvature
In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context...
of the surface of a lens
Lens (optics)
A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...
.
The usual form consists of a fine screw moving in a nut carried on the centre of a small three-legged table or frame; the feet forming the vertices of an equilateral triangle. The lower end of the screw and those of the table legs are finely tapered and terminate in hemispheres, so that each rests on a point. If the screw has two turns of the thread to the millimetre the head is usually divided into 50 equal parts, so that differences of 0.01 millimetre may be measured without using a vernier
Vernier scale
A vernier scale is an additional scale which allows a distance or angle measurement to be read more precisely than directly reading a uniformly-divided straight or circular measurement scale...
. A lens, however, may be fitted, in order to magnify the scale divisions. A vertical scale fastened to the table indicates the number of whole turns of the screw and serves as an index for reading the divisions on the head.
A contact-lever, delicate level or electric contact arrangement may be attached to the spherometer in order to indicate the moment of touching more precisely than is possible by the sense of touch. To measure the radius of a sphere—e.g. the curvature of a lens
Lens (optics)
A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...
—the spherometer is levelled and read, then placed on the sphere, adjusted until the four points exert equal pressure, and read again. The difference gives the thickness of that portion of the sphere cut off by a plane passing through the three feet.
Calling this distance h, and the distance between the feet a, the radius R is given by the formula:
Alternate uses
Since the spherometer is essentially a type of micrometerMicrometer
A micrometer , sometimes known as a micrometer screw gauge, is a device incorporating a calibrated screw used widely for precise measurement of small distances in mechanical engineering and machining as well as most mechanical trades, along with other metrological instruments such as dial, vernier,...
, it can be employed for other purposes than measuring the curvature of a spherical surface. For example, it can be used to measure the thickness of a thin plate.
To do so, the instrument is placed on a perfectly level plane surface and the screw turned until the point just touches; the exact instant when it does so is defined by a sudden diminution of resistance succeeded by a considerable increase. The divided head and scale are read; the screw is raised; the thin plate slipped under it; and the process is repeated. The difference between the two readings gives the required thickness.
Similarly, the instrument can measure the depression in an otherwise flat plate. The method would be as for measuring the thickness of a plate, except that the micrometer portion is placed over the depression and the measurement is taken below the surface instead of above.
This type of instrument is commonly seen used in inspections of oil field tool pipe for metal surface pits, fractures, and roundness before being shipped to drilling sites for exploratory wells. See drill pipe
Drill pipe
Drill pipe, is hollow, thick-walled, steel piping that is used on drilling rigs to facilitate the drilling of a wellbore and comes in a variety of sizes, strengths, and weights but are typically 30 to 33 feet in length...
. The process of inspections are designed to remove weakened tool pipe, so that pipe will not fracture during drilling. Tool pipe with thicker than 1" walls for a 4" diameter tube of hardened steel, fitted with tapered thread collars are re-used after drilling is complete, and thinner-walled tubular oil-well casing is in place. Electronic instrumentation similar to the spherometer in design are modified at inspection plants for casing, tubing, and drill pipe. The equivalent measurements in optics would be for a cylinder, or lens with a cylindrical component having an optical axis, where a plane through the lens would produce an oval circumference.