Vernier Caliper

Main Scale

Vernier (auxiliary) Scale

You will notice that one of the vernier scale one of the vernier scale divisions coincides with one of the main scale divisions coincides with one of the main scale divisions. divisions.

Principle of Vernier

N divisions on the vernier scale is equal to (N-1) divisions on the main scale.

Principle of Vernier

Least Count indicates the degree of Precision of

measurement that can be achieved by the measuring

instrument.

Suppose, Two different vernier callipers have different number of equal

divisions on their vernier scales

i) 10 equal divisions ii) 50 equal divisions.

Which can measure more precisely ?

The least count of the I vernier callipers = 1/10 =0.1mm

The least count of the II vernier callipers = 1/50 =0.02mm.

That is, the II vernier callipers with 0.02mm of L.C can measure up to

0.02mm accurately.

Hence, the precision of II vernier callipers in more than I vernier callipers.

Question: What happens if instead if N-1 divisions, the N divisions of

my vernier callipers divides N-2 or N-3 divisions on the main scale? Is it

possible? what changes should we make to find the least count? which

calliper would be more precise?

Ans: if (n-2) M.S.D = n V.S.D

Then 1 V.S.D = {(n-2)/n} M.S.D

L.C = 1 M.S.D – 1 V.S.D = 1mm – {(n-2)/n} mm = 2/n if n =10

L.C = 2/10 = 0.2 mm

i.e. when (n-1) divisions are changed to (n-2)divisions least count is

increased from 0.1mm to 0.2mm

i.e. the precision of the vernier callipers is decreased.

so, if (n-3) M.S.D s are divided in to n equal divisions on vernier scale

the L.C further increases and the precision further decreases.

Principle of Vernier

The reading on the main scale just before (LEFT) the zero of the vernier is noted. The reading on the main scale just before (LEFT) the zero of the vernier is noted. This is called Main scale reading (M.S.R).The number of division (n) on the vernier This is called Main scale reading (M.S.R).The number of division (n) on the vernier which coincides perfectly with any one of the main scale divisions is noted. This is which coincides perfectly with any one of the main scale divisions is noted. This is called vernier coincidence (V.C).The vernier coincidence (V.C=n) is multiplied by called vernier coincidence (V.C).The vernier coincidence (V.C=n) is multiplied by least count to get the fraction of a main scale division. This is added to the main least count to get the fraction of a main scale division. This is added to the main scale reading (M.S.R) scale reading (M.S.R)

Reading of the instrument Reading of the instrument = = MSR + (n x L.C.)MSR + (n x L.C.)

Reading of the instrument Reading of the instrument = = MSR + (n x L.C.)MSR + (n x L.C.)

Main Scale reading = 1.2 cm; vernier scale reading = 3×0.01 cm = 0.03 cmSo,Reading = 1.2 + 0.03 = 1.23 cm

How to take reading of a Vernier scale

1 cm1 cm

Another Example

Another Example

2.4cm2.4cm

Another Example

Click on the picture for Video on Vernier Scale

http://members.shaw.ca/ron.blond/Vern.APPLET

Java Applet for Vernier Scale

Tutor Vista animation

No zero error. Positive zero error

Zero ErrorZero ErrorWhen jaws of the vernier callipers are in contact, and if the zero division of main scale does not coincide with the zero mark on vernier scale, such vernier calipers will have zero error.

Types of Zero Error in vernier callipers

i)Negative Zero error ii) Positive Zero error

Positive zero error: When the jaws of the vernier callipers are closed,

and if the zero mark on the auxiliary (vernier) scale lies to the right of the

main scale zero-mark, then error is called Positive Zero error. So, the zero

correction should be subtracted from the reading which is measured.

Zero error = +0.01 cm

Zero error = +0.04 cm

when the jaws are closed and if the reading is 0.10mm, the zero error is referred to as +0.10mm.

'actual reading = main scale + vernier scale - (zero error)'

thus the actual reading is 19.00 + 0.54 - (0.10) = 19.44 mm

Negative zero error: When the jaws of the vernier callipers are in contact, and if the

first mark on the auxiliary (vernier) scale lies to the left of zero of main scale such an

error is called Negative Zero error. So, the zero correction should be added to the

reading which is measured.

Zero error = - 0.02 cm

Zero error = - 0.08 cm

when the jaws are closed and if the reading is -0.08mm, the zero error is referred to as -0.08mm

'actual reading = main scale + vernier scale - (zero error)'

thus the actual reading is 19.00 + 0.36 - (-0.08) = 19.44 mm