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

The instrument whose least count is minimum, is called the most precise device.

(a) Number of division (MSD) = 20

Main Scale Division (MSD) =1mm

As 20 divisions on vernier scale will be equal to the 19 divisions on main scale.

 $\therefore$Vernier Scale Division (VSD) $=\frac{19}{20}MSD$

Least count of varnier callipers =1MSD -1VSD

=1MSD -1VSD

$=1MSD-\frac{19}{20}MSD=\frac{1}{20}MSD$

$=\frac{1}{20}mm=\frac{1}{200}cm$

= 0.005 cm

(b) Pitch of screw guage =1mm

Number of divisions on circular scale =100

Least count of screw guage

$=\frac{Pitch}{Numberofdivisionsoncircularscale}$

$=\frac{1}{100}mm=\frac{1}{1000}cm$

= 0.001cm

(c) Wavelength of light $\left(\lambda \right)\approx {10}^{-7}m={10}^{-5}cm=0.00001cm$

$\therefore$As the given optical instrument can measure length to within a wavelength of light, therefore least count of the given optical instrument = Wavelength of light. = 0.00001 cm

The least count is minimum for the given optical instrument. Therefore, the given optical instrument is the most precies.