Problem 59 - Master Resource Book in JEE Main Physics

Question

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 \(1 \mathrm{~mm}\) and 100 divisions on the circular scale (c) An optical instrument that can measure length to within a wavelength of light? (d) All are equally precise device for measuring length

Step-by-Step Solution

Answer

The optical instrument is the most precise for measuring length (option c).

Step 1: Understand the Terminology

Precision is the ability of a measurement to be consistently reproduced. The device with the least count or smallest measurable unit has higher precision.

Step 2: Analyze the Vernier Callipers

A vernier calliper with 20 divisions on the sliding scale often has a least count of 0.1 mm, because its typical formula is given by \( \frac{1\text{ main scale division}}{\text{number of vernier divisions}} \). This specifies its precision.

Step 3: Analyze the Screw Gauge

A screw gauge with a pitch of 1 mm and 100 divisions has a least count of \( \frac{1}{100} \) mm or 0.01 mm. The least count is calculated using pitch divided by the number of divisions on the circular scale, indicating it is more precise than the vernier calliper.

Step 4: Analyze the Optical Instrument

An optical instrument capable of measurements within a wavelength of light can be extremely precise. Visible light wavelengths range roughly between 400 nm to 700 nm (0.0004 mm to 0.0007 mm), which is much smaller and thus more precise than the other devices.

Step 5: Make a Conclusion

Comparing all devices based on their precision, the optical instrument measures at a level finer than the other devices, which range in precision from 0.1 mm to 0.01 mm.

Key Concepts

Vernier Calipers Precision

Vernier calipers are a popular tool for measuring length, especially in engineering and laboratory settings. They consist of a main scale and a sliding vernier scale. When you use a vernier caliper, you're relying on the vernier scale to provide a more precise measurement than the main scale alone.
The precision comes from the vernier principle, which allows you to read between the lines of the main scale. In this case, a vernier caliper with 20 divisions on the sliding scale typically provides a least count of 0.1 mm. This least count refers to the smallest value that can be measured, calculated as the value of one main scale division divided by the number of vernier scale divisions.
While vernier calipers are quite precise, enabling measurements down to 0.1 mm, they are not the most precise option available compared to more refined instruments.

Screw Gauge Precision

Screw gauges are renowned for their incredible precision, especially for measuring small widths, thicknesses, or diameters. A standard screw gauge consists of a rotating thimble and a spindle that are used in conjunction with a calibrated scale.
The screw gauge precision is due to its ability to measure with a very small least count, often 0.01 mm. This is achieved through its fine calibration, wherein the pitch (distance moved per revolution) divided by the number of divisions on the circular scale dictates the least count. For a screw gauge with a 1 mm pitch and 100 divisions on the circular scale, this leads to a least count of 0.01 mm.
This means that screw gauges can provide a highly sensitive measurement, more so than vernier calipers. However, even this high precision pales in comparison to some optical instruments.

Optical Measurement Precision

Optical instruments take measurement precision to another level by operating using light's properties, often relying on the wavelength of light as a reference. These instruments are commonly used in scientific research, where extreme precision is necessary.
Optical measurement devices can often achieve a precision level within the range of light wavelengths, which can be as fine as 400 to 700 nanometers (nm), or 0.0004 to 0.0007 mm. This level of precision far surpasses mechanical tools such as vernier calipers or screw gauges.
Because light can be split into such diminutive parts, these measurements can capture the most minute of lengths, making them vital in fields where precision is paramount, like optics and material sciences.