Spherometer

A spherometer gives us the precise measurement of the radius of curvature of a sphere or any other curved surface. The radius of curvature of any given spherical mirror refers to the radius of the sphere of which this mirror is a part. Robert-Aglaé Cauchoix invented the first spherometer in 1810. Its manufacturing primarily started in the 19th century for use by opticians. Opticians and astronomers used it for grinding lenses or curved mirrors. Lenses are pieces of transparent material having specific shapes that cause light rays to bend in a particular way whenever they pass through them. Lenses can be of two types: the convex (converging) lens or the concave (diverging) lens. 

Some astronomers still grind their lenses. However, in modern times, the production of the lens is entirely automatic. The modern-day spherometers have 0.5 mm scale marked-off units. Moreover, one complete turn of the dial will represent 0.5 mm, whereas each small graduation will represent 0.05 mm. Let’s study the uses of spherometers and their structure in brief.

Parts of the spherometer

A general spherometer comprises three main parts. These three parts are as follows:

• It has a base circle with three outer legs. Moreover, it has a ring whose radius is known. 

• It consists of a central leg, which can be adjusted as per the need.

• It has a device for reading that will measure the amount of distance the central leg will move.

Spherometer

In its common form, the spherometer comprises a fine screw moving in a nut. This nut is carried to the three small legged frame’s centre. The feet form the vertices of the triangle. The lower ends of both screws and table legs terminate in the hemisphere. Moreover, each of these ends rests on a point. If the given screw consists of two turns of the thread to the micrometre (mm), then its head will usually divide into 50 equal parts. As a result, we can measure the difference of 0.01 mm without the help of a vernier calliper. To increase the magnifications of the scale division, a lens is fitted to it. The vertical scale shows the total number of turns of the screw. It will also give out the index that will help read the divisions. To indicate the moment of touching with greater accuracy than just by the sense of touch, either a contact-lever or an electric contact arrangement is attached. Level the spherometer to evaluate the radius of the sphere. After levelling, adjust it so that all four points start exerting the same pressure. Now, note the reading again. This difference will indicate the thickness of this given portion that is to be cut off.

How to use a spherometer?

The steps for using a spherometer are as follows:

• Place the instrument on the plane surface. Scew the middle foot down until it touches the surface; now, the device will turn around (on its middle foot as the centre). 

• Remove the device carefully from the glass, and then take the readings of the mm screw. 

• For a perfect instrument, the readings will be 0-0. If there is a slight error, the values will be either positive or negative.

• Remove the instrument from the plane and draw the middle foot back. 

• Measure the radius of this given sphere from its convex side. 

• Take the readings of the screw-head and the scale. 

• Either subtract the distance from the zero error or add it if the reading comes out below the zero line.

• Place the two legs on a card paper and measure their length using a metre scale.

• Now, apply the formula for determining the radius of curvature as given below:

r= I2/6a + a/2

Uses of a spherometer

Besides measuring the radius of curvature of a spherical mirror, some uses of the spherometer are as follows:

• For measuring the thickness of a thin plate

• For measuring the depression in an otherwise flat plane (for example, inspections of oil field tool pipe for metal surface pits)

• Cylindrometer (a related device to the spherometer) helps in determining the radius of curvature for a right-circular cylinder.

Conclusion

A spherometer is an instrument or device used to measure the radius of curvature of a given sphere. It gives the results with a high degree of precision and also helps in determining the thickness of the thin plates, measuring the depression in flat surfaces, etc. Most of these devices were tiny, ranging from a few (4 to 5) cm, used by opticians or lens makers for measuring the radius of curvature. They have a delicate nature and can easily bend; therefore, they usually come with a glass plate. This glass plate is used to zero the millimetre. In its typical form, the spherometer comprises a fine screw moving in a nut that is carried to the three small legged frame’s centre. The foot forms the vertices of the triangle. It also comprises a device for reading that will measure the amount of distance the central leg will move.