Spherometer

A spherometer is an instrument for the precise measurement of the radius of a sphere. Originally, these instruments were primarily used by opticians 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 500 equal parts, so that differences of 0.001 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: $R\; =\; left(\; frac\{a^2\; +\; 3h^2\}\{6h\}\; ight)$

Alternate uses

Since the spherometer is essentially a type of micrometer, 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.

ee also

*Lens clock
*Vertometer
*Lensmeter

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