Deeper Grating Scans

Grating Wavelength Three-Row Scan

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.

5 m⋅15=1 mmλ=1⋅1 m=1 mA=15\ \text{m}\cdot\frac{1}{5}=1\ \text{m}\quad m\lambda=1\cdot1\ \text{m}=1\ \text{m}\quad A=1
Grating relation rowThe grating spacing, sine marker, order, wavelength, and acceptance bit are checked.sinegratingSpacing=5 msineFactor=1/5wavelength=1 morder=1 countacceptedBit=1 bit

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.

5 m⋅25=2 mmλ=1⋅2 m=2 mA=15\ \text{m}\cdot\frac{2}{5}=2\ \text{m}\quad m\lambda=1\cdot2\ \text{m}=2\ \text{m}\quad A=1
Grating relation rowThe grating spacing, sine marker, order, wavelength, and acceptance bit are checked.sinegratingSpacing=5 msineFactor=2/5wavelength=2 morder=1 countacceptedBit=1 bit

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.

5 m⋅1=5 mmλ=1⋅3 m=3 mA=05\ \text{m}\cdot1=5\ \text{m}\quad m\lambda=1\cdot3\ \text{m}=3\ \text{m}\quad A=0
Grating relation rowThe grating spacing, sine marker, order, wavelength, and acceptance bit are checked.sinegratingSpacing=5 msineFactor=1wavelength=3 morder=1 countacceptedBit=0 bit