Calculate the calibration factor using the provided micrometer measurements.

Question

ScanSolve AI Tutor · Accepted Answer

To find the calibration factor, we need to determine the actual length represented by one division of the eyepiece micrometer. This is done by comparing the eyepiece micrometer to a stage micrometer, which has known divisions.

Determine the value of one small division on a standard stage micrometer.
A standard stage micrometer has divisions where each small division is $0.01 \, \text{mm}$ .
Convert the value of one small stage micrometer division to microns.
Since $1 \, \text{mm} = 1000 \, \mu\text{m}$ ,
$0.01 \, \text{mm} = 0.01 \times 1000 \, \mu\text{m} = 10 \, \mu\text{m}$
Calculate the total length represented by the coinciding stage micrometer divisions.
The problem states that 20 small stage micrometer divisions coincided.
Total length = $20 \, \text{divisions} \times 10 \, \mu\text{m}/\text{division} = 200 \, \mu\text{m}$
Calculate the calibration factor for one eyepiece micrometer division.
The problem states that 80 small eyepiece micrometer divisions coincided with the 20 small stage micrometer divisions.
So, 80 eyepiece divisions = $200 \, \mu\text{m}$ .
The calibration factor is the value of one eyepiece division:
$\text{Calibration Factor} = \frac{\text{Total length of stage micrometer divisions}}{\text{Number of coinciding eyepiece micrometer divisions}}$ $\text{Calibration Factor} = \frac{200 \, \mu\text{m}}{80}$ $\text{Calibration Factor} = \frac{20}{8} \, \mu\text{m}$ $\text{Calibration Factor} = 2.5 \, \mu\text{m}$
The correct option is 2.5.
$\text{2.5}$

Calculate the calibration factor using the provided micrometer measurements.

Answer

Step-by-step solution

Determine the value of one small division on a standard stage micrometer.

Convert the value of one small stage micrometer division to microns.

Calculate the total length represented by the coinciding stage micrometer divisions.

Calculate the calibration factor for one eyepiece micrometer division.

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