Vernier Calipers
Study guide, definitions & notes
1 Introduction
Any experimental science must include measurement as a core component,
and physics is no exception. One quantifiable metric that we commonly need
to measure among the others is length. At one extreme, the size of our huge
cosmos allows us to measure distances in terms of light-years, which are so
far away that we cannot see them with our eyes. The other end of the lowest
distances is being pushed down to a fermi (which is 10-15 m) or even lower
by recent findings. Again, these distances are so minuscule that our eyes are
unable to detect them. At every 1 to 2 order of magnitude change in
distances, our instruments to measure them accurately can differ. When
the distances that we want to measure, are in the range of 10−2 mm to 1
mm, we use Vernier calipers and Screw Gauge for precise measurement. In
this handout, Vernier calipers and associated ideas are discussed.
2 Details of the Instrument
In 1631, Pierre Vernier of France invented Vernier calipers, a device for
taking extremely precise linear measurements. Vernier calipers are
frequently used for quality control measures in industrial and scientific
facilities.
, There is a main scale which is graduated in cm (labeled by 4) on one side
and in inch (labeled by 5) on the other side. Clamped on the main scale,
there is a Vernier scale (6 or 7) that can be moved along the main scale.
There are two jaws. The outside jaws (1) which can be used to measure
outer dimensions of objects, e.g. the length of a rod, the diameter of a
cylindrical or spherical object, edge length of cube etc. and the inside
jaws (2) that are useful in measuring internal diameter of hollow
cylindrical objects or pipes. The depth probe or the depth strip (3) can
be used to measure the depth of objects like beakers. The retainer (8) is
spring loaded and is used to stop the movable parts from moving.
2.1 Least Count of the instrument
Observing carefully, we find that one main scale division (MSD) does not have
the same length as one Vernier scale division (VSD). In fact, with the 0th mark
of the main scale aligned with the 0th mark of the Vernier scale, the 9th mark
of the main scale coincides with the 10th mark of the Vernier scale. That is, 9
MSD = 10 VSD. This means that 1 VSD = 9/10 MSD. Since 1 MSD is equal to 1
mm. This means that 1 VSD = 0.9 mm. The least count (LC for short) is defined
as the difference between the length of one main scale division and the
length of one Vernier scale division, i.e.
LC = 1 MSD − 1 VSD = 1 mm − 0.9 mm = 0.1 mm = 0.01 cm
Hence, the least count of Vernier calipers is 0.01 cm, i.e. it can measure up to
a 100th of a centimeter.
2.2 Zero Error
Normally, with the jaws closed the 0th mark of the main scale should
coincide with the 0th mark of the Vernier scale as has been shown in
Figure (1a). However, due to various reasons, it might happen that with
the two jaws closed, the 0th marks of the two scales do not coincide. We
then say that the Vernier caliper has a zero error. If the 0th mark of the
Vernier scale is slightly to the right of the 0th mark of the main scale, as
Study guide, definitions & notes
1 Introduction
Any experimental science must include measurement as a core component,
and physics is no exception. One quantifiable metric that we commonly need
to measure among the others is length. At one extreme, the size of our huge
cosmos allows us to measure distances in terms of light-years, which are so
far away that we cannot see them with our eyes. The other end of the lowest
distances is being pushed down to a fermi (which is 10-15 m) or even lower
by recent findings. Again, these distances are so minuscule that our eyes are
unable to detect them. At every 1 to 2 order of magnitude change in
distances, our instruments to measure them accurately can differ. When
the distances that we want to measure, are in the range of 10−2 mm to 1
mm, we use Vernier calipers and Screw Gauge for precise measurement. In
this handout, Vernier calipers and associated ideas are discussed.
2 Details of the Instrument
In 1631, Pierre Vernier of France invented Vernier calipers, a device for
taking extremely precise linear measurements. Vernier calipers are
frequently used for quality control measures in industrial and scientific
facilities.
, There is a main scale which is graduated in cm (labeled by 4) on one side
and in inch (labeled by 5) on the other side. Clamped on the main scale,
there is a Vernier scale (6 or 7) that can be moved along the main scale.
There are two jaws. The outside jaws (1) which can be used to measure
outer dimensions of objects, e.g. the length of a rod, the diameter of a
cylindrical or spherical object, edge length of cube etc. and the inside
jaws (2) that are useful in measuring internal diameter of hollow
cylindrical objects or pipes. The depth probe or the depth strip (3) can
be used to measure the depth of objects like beakers. The retainer (8) is
spring loaded and is used to stop the movable parts from moving.
2.1 Least Count of the instrument
Observing carefully, we find that one main scale division (MSD) does not have
the same length as one Vernier scale division (VSD). In fact, with the 0th mark
of the main scale aligned with the 0th mark of the Vernier scale, the 9th mark
of the main scale coincides with the 10th mark of the Vernier scale. That is, 9
MSD = 10 VSD. This means that 1 VSD = 9/10 MSD. Since 1 MSD is equal to 1
mm. This means that 1 VSD = 0.9 mm. The least count (LC for short) is defined
as the difference between the length of one main scale division and the
length of one Vernier scale division, i.e.
LC = 1 MSD − 1 VSD = 1 mm − 0.9 mm = 0.1 mm = 0.01 cm
Hence, the least count of Vernier calipers is 0.01 cm, i.e. it can measure up to
a 100th of a centimeter.
2.2 Zero Error
Normally, with the jaws closed the 0th mark of the main scale should
coincide with the 0th mark of the Vernier scale as has been shown in
Figure (1a). However, due to various reasons, it might happen that with
the two jaws closed, the 0th marks of the two scales do not coincide. We
then say that the Vernier caliper has a zero error. If the 0th mark of the
Vernier scale is slightly to the right of the 0th mark of the main scale, as
