Question

(i)Which of the following is the most precise device for measuring length
a vernier callipers with $20$ divisions on the sliding scale

(ii)Which of the following is the most precise device for measuring length
a screw gauge of pitch $1\text{mm}$ and $100$ divisions on the circular scale

(iii)Which of the following is the most precise device for measuring length
an optical instrument that can measure length to within a wavelength of light?

Answer 1

(i) Given: Instrument used- Vernier callipers
Least count $=1MSD-1VSD$
$=1MSD-\frac{19}{20}MSD=\frac{1}{20}MSD$

$=\frac{1}{20}\text{mm}=\frac{1}{200}\text{cm}=0.005\text{cm}$

(ii) Given: Instrument used- Screw gauge
$\lambda \approx {10}^{-5}\text{cm}$
$=0.00001\text{cm}$
$\therefore LC=0.00001\text{cm}$

(iii) Least count of optical device=
wavelength of light ~${10}^{-5}$ cm= 0.00001 cm

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