Grating Spacing Three-Row Scan - Optics Step by Step

A grating-spacing scan varies the line spacing d across three rows at fixed wavelength 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 spacings, orders, wavelengths, 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.

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\ \text{m}\cdot1=4\ \text{m}\quad m\lambda=2\cdot2\ \text{m}=4\ \text{m}\quad A=1

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\ \text{m}\cdot\frac{4}{5}=4\ \text{m}\quad m\lambda=2\cdot2\ \text{m}=4\ \text{m}\quad A=1

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\ \text{m}\cdot\frac{2}{5}=4\ \text{m}\quad m\lambda=2\cdot2\ \text{m}=4\ \text{m}\quad A=1