This presentation explains about the usage of a spherometer to take measurements. First part includes the definition and the description of its parts while the second part explains as to how different measurements can be taken.

1. SPHEROMETER
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By Aditya Abeysinghe

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3. Spherometers are small precision instruments for
measuring the radius of curvature of spherical
surfaces. They can also be used to measure the
thickness of a thin plate.
INTRODUCTION

4. PARTS OF A SPHEROMETER
Reading for convex
surfaces
Zero of vertical scale
Reading for concave
surfaces
Circular
scale
Legs
Central leg or
middle screw
Base circle
Screw head

5. Pitch- Pitch is the distance moved by the middle
screw per revolution
Pitch may vary for different spherometers
Least count = Pitch / No.of divisions on the circular
scale
E.g.: The least count for a spherometer of 100 equal
divisions and of pitch 0.5 mm is,
Least count = 0.5mm/100 =0.005mm
SPECIAL DEFINITIONS ON
SPHEROMETER MEASUREMENTS

6. Radius of curvature of a curved mirror is the radius
of the sphere that was used to make it.
RADIUS OF CURVATURE
R
C
R – Radius of curvature
C- Center of the sphere
To measure the radius of
curvature, we place the spherometer
on the mirror as follows:

7. BUILDING AN EXPRESSION
FOR THE MEASUREMENTS
When you keep the spherometer on the
mirror it will be as follows:
h
R
R
R - h
x
From Pythagoras
theorem,
R2 = x2+ (R-h)2
R2 = x2+ R2 + h2 - 2Rh
R = (x2+ h2 ) / 2h
*However, practically, it’s
hard to measure x. So,
what we do is that we
express the above
relationship using the
distance between the legs.

8. When you keep the spherometer on any
surface, the legs will form an equilateral traingle.
See figure below.
If we take the
distance
between legs
to be ‘a’
a
a/2 a/2
30°
x
Finally you can simplify the shape to -
x
a/2
30°
Therefore,
x cos 30° = a/2
Thus, x = a / √3
Now, R = (x2+ h2 ) / 2h
By substituting for x,
R = ((a / √3 )2 + h2 ) / 2h
Therefore, R = (a2/6h) + (h/2)

9. Now that we have built a relationship for R, we can
measure R of both concave and convex surfaces
RADIUS OF CURVATURES
h
R
R
R - h
x
For convex surfaces For concave surfaces
x h
R
R
R - h

10. 1. Place the spherometer on a plane mirror and
adjust the center leg or the screw so that the
screw and the three legs are on the same
plane.(It’s always better to check whether the
object and the image are in contact on keeping
on the plane mirror)
MEASURING USING A SPHEROMETER
Matching
Not
matching

11. 2. Then read the measurement, as placed in step 1,
using the vertical and circular scales. Take this to be
x.
3. Then keeping the 3 legs in place, move the screw
upwards so that the object to be measured now is
below the screw.
4. Then adjust the screw so that the screw is just
touching the surface of the object to be measured.
5. Then take the reading at that instance using the
vertical and circular scales. Take this to be y.
6. Thus, the height of the object is the difference
between these heights.
Therefore, h = y – x.

12. 7. Now to measure the radius of curvature, if the
object used is a spherical object, first measure the
distance between the legs using a vernier caliper
(Using a vernier caliper is recommended as the
object can be tightly placed between its outer jaws)
8. Finally, use the formula derived for R to find the
radius of curvature.