A grating-sine-marker scan holds the spacing, order, and wavelength fixed and varies the sine marker across three rows, checking that only the value closing d * sin(theta) = m * lambda is accepted row by row. The arithmetic is exact only for the stated orders, spacings, wavelengths, sine markers, and rows in the ideal coherent-grating model. Real observations add alignment, finite slit/aperture size, coherence/bandwidth, detector calibration, grating imperfections, peak fitting, finite precision, and measurement uncertainty.
Only one sine marker closes the selected spacing, order, and wavelength. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Low sine marker undershoots the target
Spacing 10 m times sine marker 1/5 gives 2 m. Order 2 times wavelength 2 m gives 4 m, so this row is rejected.
10m⋅51=2mmλ=2⋅2m=4mA=0
Middle sine marker closes exactly
Spacing 10 m times sine marker 2/5 gives 4 m. Order 2 times wavelength 2 m gives 4 m, so this row is accepted.
10m⋅52=4mmλ=2⋅2m=4mA=1
High sine marker overshoots the target
Spacing 10 m times sine marker 3/5 gives 6 m. Order 2 times wavelength 2 m gives 4 m, so this row is rejected.