Question

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

• 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 division on the circular scalem
• D. An optical instrument that can measure length to within a wavelength of light

Answer 1

Answer: (D)

An optical instrument that can measure length to within a wavelength of light

Answer 2

The most precise device is one whose least count is the least.

(1) Least count of vernier calipers

$= 1MSD - 1VSD = 1MSD - \frac{19}{20}MSD = \frac{1}{20}MSD = \frac{1}{20}mm = \frac{1}{200}cm = 0.005cm$

($\because 1MSD = 1mm$)

(2) Least count of screw gauge

$= \frac{Pitch}{No.ofdivisiononcircularscale}$

$= \frac{1}{100}mm = \frac{1}{1000}cm = 0.001cm$

(3) Least count of spherometer

$= \frac{Pitch}{No.ofdivisionsoncircularscale} = \frac{0.1mm}{100} = \frac{1}{1000}mm = 0.0001cm$

(4) Wavelength of light , $\lambda \approx 10^{- 5}$cm= $0.00001cm$Clearly the optical instrument is the most precise.