Correct an instrument offset with separate evidence

Distinguish a sample mismatch from an instrument offset

Select record D and inspect its first raw center, 390.90 nm. Under the provisional zero-offset comparison it does not match a selected reference within ±0.10 nm. Reveal all features: the second raw center, 488.13 nm, also leaves no compatible single-species explanation in the selected reference set.

Do not fix the mismatch by assuming the sample must be hydrogen and shifting the observations until that identity fits. That would use the desired conclusion as the calibration evidence. Instead, reveal the independent instrument check in the final evidence stage.

The supplied calibration standards have stipulated true positions 500.00 and 600.00 nm. The instrument records them at 502.00 and 602.00 nm for D. These fictional standards are instrument checks, not additional atomic transitions claimed from a source database.

Calculate the correction from both standards

For each standard, compute recorded minus stipulated position. The first gives 502.00 − 500.00 = +2.00 nm; the second gives 602.00 − 600.00 = +2.00 nm. Both support the same additive instrument offset in this teaching model.

Corrected wavelength equals raw wavelength minus the offset. Thus D’s centers become 390.90 − 2.00 = 388.90 nm and 488.13 − 2.00 = 486.13 nm. The raw values remain in the ledger. A correction adds an interpretation layer; it does not rewrite the instrument record as though it originally read the corrected value.

Compare the corrected pair with the selected H I references 388.9049 and 486.12786 nm. Their residuals are −0.00490 and +0.00214 nm. The independently supported correction restores hydrogen compatibility under the selected-line hypothesis. NIST hydrogen air-wavelength table.

Correct the coverage along with the features

D’s raw covered interval is 382–682 nm. Subtracting the same +2 nm offset gives a corrected interval of 380–680 nm. Correcting the markers but leaving the axis coverage in the raw coordinate system would mix two wavelength scales.

Draw two aligned paper axes: raw above and corrected below. Mark both features, both interval endpoints and the calibration standards. Label the displacement as an instrument correction. The first raw feature is outside the narrow 388.4–389.4 nm detail inset; it should not be squeezed into that inset merely to make the comparison look closer.

Before the calibration stage, the display’s zero-offset calculation is provisional. “Unknown calibration” does not mean “calibration verified to be zero.” After the calibration stage, the stipulated offset is known within this exercise. That change in evidence can restore candidates, so candidate elimination need not be monotonic across all stages.

Keep instrumental and astrophysical explanations separate

An instrument offset and a physical shift of source wavelengths are different hypotheses. This exercise establishes an additive correction from standards independently of the unknown sample. It does not calculate a radial velocity or establish that the source is stationary in every physical sense.

A common additive displacement is not automatically an astrophysical Doppler shift. Motion-related interpretations require an appropriate wavelength relation and independently controlled instrumental effects. The browser contains no such velocity analysis. Its reference values also use air wavelengths consistently; changing conventions would be another source of mismatch to investigate, not evidence of motion by itself.

Real calibration has uncertainty and may require a correction that varies with wavelength. Here both standards must imply the same offset, treated as exact for the authored example. The ±0.10 nm feature tolerance is separate from that calibration assumption and from NIST’s reference uncertainties. The NIST handbook supplies selected reference facts, not a guarantee about this fictional instrument.

Transfer to inconsistent standards

A new instrument records the 500.00 nm standard at 502.00 nm and the 600.00 nm standard at 603.00 nm. A learner proposes subtracting their average offset, 2.50 nm, and calling the record calibrated under this model. Is that justified?