The thickness of a glass slide is measured with a micrometer

PHYSICS · Subjective · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Uncertainty in measurement

Measurement and Method, Ch Type A, Type B and the uncertainty budget

Problem

The thickness of a glass slide is measured with a micrometer. A complete uncertainty budget with five rows (the scatter of repeated closures, the micrometer's resolution, a bound on parallax in reading the scale, a zero-point comparison from repeated closures on the empty jaws, and a bound on thermal expansion) combines to

u_{\rm c} = 0.0034\,\mathrm{mm}

. The result is quoted as

t = (0.502 \pm 0.0068)\,\mathrm{mm}

k=2

. A laboratory report adds this comment:'(i) At

k=2

the quoted interval has

95\%

coverage, because that is what a coverage factor of

2

always means. (ii) Because the budget has five rows and accounts for every effect the experimenters could think of, the true thickness is guaranteed to lie inside

(0.502 \pm 0.0068)\,\mathrm{mm}

. (iii) The expanded uncertainty

U = 0.0068\,\mathrm{mm}

is a more careful, more trustworthy uncertainty than

u_{\rm c} = 0.0034\,\mathrm{mm}

, since it has been expanded to take extra care.'Which of the following is the correct assessment of statements (i), (ii) and (iii)? (a) (i), (ii) and (iii) are all correct as stated. (b) Only (i) is correct; (ii) and (iii) are wrong. (c) Only (ii) is correct; (i) and (iii) are wrong. (d) None of (i), (ii), (iii) is correct as stated.

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