Question

# Which of the following is the most precise device for measuring length?A. A vernier caliper with 20 divisions on the sliding scale.B. A screw gauge of pitch 1mm and 100 divisions on the circular scale.C. An optical instrument that can measure length to within a wavelength of light.D. All instruments have the same precision.

Hint: In the science of measurement, the least count of a measuring instrument is the smallest and accurate value in the measured quantity that can be resolved on the instrument’s scale.

Complete Step by step solution:
The smallest value that can be measured by the measuring instrument is called its least count. Measured values are good only up to this value. The least count error is the error associated with the resolution of the instrument
The device having a minimum least count is more accurate. The more accurate the device the minimum the least count should be.
For vernier calipers with 20 divisions on the sliding scale
The least count is
$L.C = \dfrac{1}{{20}}mm \\ = 0.05mm \\$
For screw gauge of pitch 1mm and 100 divisions on the circular scale
The least count is
$L.C = \dfrac{{1mm}}{{100}} \\ = 0.01mm \\$
For optical instrument that can measure length to within a wavelength of light
Wavelength of light is $\approx 590nm$
So the optical can measure upto $\approx 590nm$
Thus the optical instrument is having the minimum least count among all the instruments listed.
So the optical instrument is most precise of all the listed instruments.

Note: Please make sure to calculate the least count accurately in accordance to the number of divisions provided on the instrument because this will be a deciding factor in knowing how accurate the instrument is.