Deeper Grating Scans

Grating Spacing Three-Row Scan

Wider grating spacing lowers the sine marker for the same 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

Small spacing reaches the endpoint marker

Spacing 4 m times sine marker 1 gives 4 m. Order 2 times wavelength 2 m gives 4 m, so this row is accepted.

4 m⋅1=4 mmλ=2⋅2 m=4 mA=14\ \text{m}\cdot1=4\ \text{m}\quad m\lambda=2\cdot2\ \text{m}=4\ \text{m}\quad A=1
Grating relation rowThe grating spacing, sine marker, order, wavelength, and acceptance bit are checked.sinegratingSpacing=4 msineFactor=1wavelength=2 morder=2 countacceptedBit=1 bit

Wider spacing lowers the sine marker

Spacing 5 m times sine marker 4/5 gives 4 m. Order 2 times wavelength 2 m gives 4 m, so this row is accepted.

5 m⋅45=4 mmλ=2⋅2 m=4 mA=15\ \text{m}\cdot\frac{4}{5}=4\ \text{m}\quad m\lambda=2\cdot2\ \text{m}=4\ \text{m}\quad A=1
Grating relation rowThe grating spacing, sine marker, order, wavelength, and acceptance bit are checked.sinegratingSpacing=5 msineFactor=4/5wavelength=2 morder=2 countacceptedBit=1 bit

Double spacing halves the marker again

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.

10 m⋅25=4 mmλ=2⋅2 m=4 mA=110\ \text{m}\cdot\frac{2}{5}=4\ \text{m}\quad m\lambda=2\cdot2\ \text{m}=4\ \text{m}\quad A=1
Grating relation rowThe grating spacing, sine marker, order, wavelength, and acceptance bit are checked.sinegratingSpacing=10 msineFactor=2/5wavelength=2 morder=2 countacceptedBit=1 bit