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 $1mm$ and $100$ divisions on the circular scale
• C. A spherometer of pitch $0.1mm$ and $100$ divisions on the circular scale
• D. An optical instrument that can measure length to within a wavelength of light

Answer 1

Answer: (D)

(a) Least count of vernier callipers
$=1MSD-1VSD=1MSD-\frac{19}{20}MSD$
$=\frac{1}{20}MSD=\frac{1}{20}mm=\frac{1}{200}cm=0.005cm$
$\left(\because 1MSD=1mm\right)$
(b) Least count of screw gauge
$=\frac{\text{Pitch}}{\text{No.of divisions on circular scale}}$
$=\frac{1}{100}mm=\frac{1}{1000}cm$
$=0.001cm$
(c) Least count of spherometer
$=\frac{\text{Pitch}}{\text{No.of divisions on circular scale}}$
$=\frac{0.1mm}{100}=\frac{1}{1000}mm$
$=0.0001cm$
(d) Wavelength of light, $\lambda =10^{-5}cm=0.00001cm$
Clearly the optical instrument is the most precise.