# Q 2.6: Which of the following is the most precise device for measuring length :(a) a vernier callipers with 20 divisions on the sliding scale(b) a screw gauge of pitch 1 mm and 100 divisions on the circular scale(c) an optical instrument that can measure length to within a wavelength of light?

To judge which tool is more precise, we have to find out their least count. Least count defines the margin of error and hence the precision. Hence the instrument with lower least count will be more precise.

(a) Least count = $1MSD - 1VSD = 1 - (19/20)= 1/20 = 0.05\ cm$   (Taking 1 MSD as 1 mm)

(b) Least count = pitch/ number of divisions

$1/10000 = 0.001 cm$

(c) least count = wavelength of light = 400nm to 700nm, that is in the range of $10^{-7}$ m

Therefore, the optical instrument is the most precise device used to measure length.

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