Question

Which of the following is the most precise device for measuring length:

1. a vernier callipers with 20 divisions on the sliding scale
2. a screw gauge of pitch 1 mm and 100 divisions on the circular scale
3. an optical instrument that can measure length to within a wavelength of light?

Answer 1

A device with minimum count is the most suitable to measure length.

(a) Least count of vernier callipers

= 1 standard division (SD) – 1 vernier division (VD)

= `1-19/20 = 1/20 "mm"`

= `1/200 "cm"`

= 0.005 cm

(b) Least count of screw gauge  = `"Pitch"/"Number of division"`

= `1/1000`

= 0.001 cm

(c) Least count of an optical device = Wavelength of light ∼ 10^–5 cm

= 0.00001 cm

Hence, it can be inferred that an optical instrument is the most suitable device to measure length.