Question

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

a vernier calipers with 20 divisions on the sliding scale  
a screw gauge of pitch 1 mm and 100 divisions on the circular scale
an optical instrument that can measure length to within a wavelength of light ?

Answer 1

Given measuring devices:

• Vernier calipers with 20 divisions on the sliding scale
• Screw gauge with pitch 1 mm and 100 divisions on the circular scale
• An optical instrument that can measure length to within a wavelength of light

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Step 1: Compare least counts (precision)

(i) Vernier calipers

Least count of a vernier calipers:

LC = 1 MSD / number of vernier divisions

Assuming 1 main scale division (MSD) = 1 mm,

LC = 1 / 20 = 0.05 mm

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(ii) Screw gauge

Least count of a screw gauge:

LC = Pitch / number of circular scale divisions

LC = 1 mm / 100 = 0.01 mm

So, the screw gauge is more precise than the vernier calipers.

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(iii) Optical instrument

The optical instrument can measure length to within a wavelength of light.

Typical wavelength of visible light:

λ ≈ 5 × 10⁻⁷ m = 0.0005 mm

This is much smaller than the least counts of both vernier calipers and screw gauge.

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Step 2: Final comparison

• Vernier calipers: least count ≈ 0.05 mm
• Screw gauge: least count ≈ 0.01 mm
• Optical instrument: least count ≈ 5 × 10⁻⁷ m

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Final Answer:

The optical instrument that can measure length to within a wavelength of light is the most precise device.