Spherometer

A spherometer is an instrument for the precise measurement of the radius of curvature of a sphere or a curved surface. 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 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.

The spherometer directly measures a sagittal, h. Using the mean length between two outer legs, a, the spherical radius R is given by the formula:

Using different spherometer without legs and with circle cup and dial gauge, D is the diameter of circle cup, the spherical radius R is given by the formula:

A spherometer basically is a precision instrument to measure very small lengths. Its name reflects the way it is used to measure the radii of curvature of spherical surfaces. It is based on the principle of screw. In general the spherometer consists of:

Since the spherometer is essentially a type of micrometer, it can be employed for purposes other than measuring the curvature of a spherical surface. For example, it can be used to measure the thickness of a thin plate.

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