Which of the following is the most precise device for measuring length : (a) a vernier callipers with 20 divisions on the sliding scale (b) a screw gauge of pitch 1 mm and 100 divisions on the circular scale (c) an optical instrument that can measure length to within a wavelength of light ?

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Solution

The instrument that has minimum least count is the most precise.

(a)

Given, the number of divisions on the sliding scale for a Vernier caliper is 20.

The least count of the Vernier caliper is,

Least count= one main scale division number of division on main scale

Substitute the given value in the above expression.

Least count= 1 mm 20 =0.05 mm

(b)

Given, the number of divisions on the circular scale for a screw gauge is 100 and pitch of the screw gauge is 1 mm

The least count of the screw gauge is,

Least count= pitch number of division on circular scale

Substitute the given value in the above expression.

Least count= 1 mm 100 =0.001 mm

(c)

Given, the optical instrument measures the length within a wavelength of light. The average wavelength of light is approximately 600 nm .

The least count of the optical instrument is,

Least count=wavelength of light

Substitute the given value in the above expression.

Least count=600 nm× 10 −6 mm 1 nm =0.0006 mm

Since the least count of the optical instrument is minimum as compared to the least count of the Vernier calipers and screw gauge. So the optical instrument is more precise to measure the length. Hence, the correct option is (c).

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