A grating-wavelength scan varies the wavelength across three rows at fixed spacing and order, showing how the order angle moves through d * sin(theta) = m * lambda row by row. The arithmetic is exact only for the stated wavelengths, spacings, orders, 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.
Longer wavelength raises the sine marker for the same spacing and order. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Short wavelength closes at one fifth
Spacing 5 m times sine marker 1/5 gives 1 m. Order 1 times wavelength 1 m gives 1 m, so this row is accepted.
5m⋅51=1mmλ=1⋅1m=1mA=1
Double wavelength doubles the marker
Spacing 5 m times sine marker 2/5 gives 2 m. Order 1 times wavelength 2 m gives 2 m, so this row is accepted.
5m⋅52=2mmλ=1⋅2m=2mA=1
Endpoint sine overshoots this wavelength
Spacing 5 m times sine marker 1 gives 5 m. Order 1 times wavelength 3 m gives 3 m, so this row is rejected.