Question

Which of the following instruments has minimum least count?

• A. A vernier callipers with 20 divisions on the vernier scale coinciding with 19 main scale divisions.
• B. A screw gauge of pitch 1 mm and 100 divisions on the circular scale.
• C. A spherometer of pitch 0.1 mm and 100 divisions on the circular scale.
• D. An optical instrument that can measure length to within a wavelength of light.

Answer 1

The correct option is D An optical instrument that can measure length to within a wavelength of light.

(a) Least count of vernier callipers
=1 MSD - 1 VSD = 1 MSD - $\frac{19}{20}$ MSD
=$\frac{1}{20}MSD=\frac{1}{20}mm=\frac{1}{200}cm=0.005cm(\because 1MSD=1mm)$
(b) Least count of screw gauge
= $\frac{Pitch}{No.ofdivisionsoncircularscale}$
$\frac{1}{100}mm=\frac{1}{100}cm=0.001cm$
(c) Least count of spherometer
= $\frac{Pitch}{No.ofdivisionsoncircularscale}$
$\frac{0.1mm}{100}=\frac{1}{1000}mm=0.0001cm$