A Spherometer is an instrument for measuring the curvature of a surface. The Spherometer is a device use in measuring the radius of curvature of a spherical surface.
For example, it can be used to measure the thickness of a microscope slide or the depth of depression in a slide.
Even the curvature of a ball can be measured using a Spherometer.
The Spherometer consists of a micrometer screw threaded into a small tripod with a vertical scale fastened to it.
The head of the screw has a graduated disk used to measure fractional turns of the screw.
The vertical scale is used to measure the height or depth of the curvature of the surface.
The vertical scale divisions are on 1 mm, which is the pitch of the threads of the screw.
The head of the screw is graduated into 100 divisions.
Aldis's Spherometer
A spherometer is an instrument that measures the sag of a surface with great precision.
A common spherometer is the Aldis spherometer in which three small balls are arranged to form an equilateral triangle. In the center of the triangle there is a probe mounted on a micrometer.
Schematic diagram of a spherometer
MEASURING THE RADIUS OF CURVATURE BY MEANS OF A SPHEROMETER
I. Description of the Spherometer
A spherometer is a precision instrument to measure very small lengths. Its name reflects the way it is used to measure the radius of curvature of spherical surfaces.
In general the spherometer consists of:
A. A base circle of three outer legs, a ring, or the equivalent, having a known radius of the base circle. Note that the outer legs of the spherometer shown can be moved to the inside set of holes in order to accommodate a small lens.
This is also trueof the old spherometer in the lab.
B. A central leg, which can be raised or lowered.
C. A reading device for measuring the distance the central leg is moved.
On the new spherometer, the vertical scale is marked off in units of 0.5 mm.
One complete turn of the dial also corresponds to 0.5 mm and each small graduation on this dial represents 0.005 mm. The small graduations on the old spherometer are 0.001 mm.
See the diagram.
II. Theory
Diagram for spherometer calculation.
Consider a circle where the distance DE is a diameter which bisects the chord AC .
See Figure 2. If we know the distance DBand BC we can find the radius of the circle as follows:
From geometry (similar triangles) we have
where R is the radius of the circle as shown in the diagram
III. Measuring the Radius of Curvature, R
The outer (fixed) legs of the spherometer determine the distance BC .
This is simply the radius of the circle formed by the legs.
To find this radius,
measure the distance from the central leg (when it is coplanar with the other
legs) to any of the outer legs. This distance is shown in the schematic diagram
r = BC
The distance BD is determined from the distance the central leg moves.
First determine the position of the central leg when it is coplanar with the outer legs by using the flat provided. (For the new spherometer, a "rocking" technique is suggested. The center leg of the spherometer is pressure sensitive and mechanically moves a lever arm that raises a piece of wire.)
Next, find the position of the central leg on the surface being measured.
The difference between these two positions is the shift of the central leg h which is equal to DB in the calculation diagram.
Our equation now reads:
R = r2/2h + h/2
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