. . . g o i n g o n e s t e p f u r t h e r
r
h
R h
-
R
r
h
R h
-
R
s
r
BAS IC PRINC IPLES
A spherometer consists of a tripod with the three legs tipped
by steel points and forming an equilateral triangle with sides
of 50 mm. A micrometer screw, the tip of which is the point to
be measured, passes through the centre of the tripod. A verti-
cal rule indicates the height
h
of the measured point above a
plane defined by the tips of the three legs. The height of the
measured point can be read off to an accuracy of 1 μm with the
aid of a circular scale that rotates along with the micrometer
screw.
The relationship between the distance
r
of all three legs from the
centre of the spherometer, the radius of curvature
R
to be deter-
mined and the height
h
of the surface is given by the following
equation:
(1)
Rearranging for
R
gives:
(2)
The distance
r
can be calculated from the length
s
of the sides of
the equilateral triangle formed by the legs:
(3)
Thus the relevant equation for
R
is as follows:
(4)
( )
2
2 2
h R r R
−
+
=
h
h r
R
⋅
+
=
2
2
2
3
s
r
=
2 6
2
h
h
s
R
+
⋅
=
Schematic for measurement of radius of curvature by means of a spherometer
Top:
Vertical cross section for measuring an object with a convex surface
Middle: Vertical cross section for measuring an object with a concave surface
Bottom: View from above
EVALUATION
The separation
s
between the legs of the spherometer is in this
case 50 mm. When the height
h
is small, equation (4) can be sim-
plified to the following:
The scale of the spherometer allows readings for heights between
10 mm and 1 μm to an accuracy of 1 μm, so that radii of curva-
ture of about 40 mm to 400 m can be calculated.
h
h
h
s
R
2
2
2
mm
420
6
mm 2500
6
≈
⋅
=
⋅
=
UE101010
Spherometer
Mechanic s / Me a surement procedure s
