young-fringe-relation-cross-scan - Wave Optics: Interference and Diffraction Step by Step

The Young-fringe formula is scanned through order and screen distance, with three exact rows for each relation. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Start from one checked Young row

The relation is a screen-position ledger. Wavelength, screen distance, slit spacing, and order are all pinned before any trend is read.

y=\frac{m\lambda L}{d}=\frac{1\cdot2\ \text{m}\cdot6\ \text{m}}{3\ \text{m}}=4\ \text{m}

Order sweep: three orders, same geometry

Hold wavelength, screen distance, and slit spacing fixed. The three-row scan shows that screen position follows the order count directly.

\begin{array}{c|c|c|c|c}m&\lambda&L&d&y\\1&2\ \text{m}&6\ \text{m}&3\ \text{m}&4\ \text{m}\\2&2\ \text{m}&6\ \text{m}&3\ \text{m}&8\ \text{m}\\3&2\ \text{m}&6\ \text{m}&3\ \text{m}&12\ \text{m}\\\end{array}

Screen sweep: three distances, same first order

Hold the first bright order and slit spacing fixed. Moving the screen farther out moves the fringe position by the same factor.

\begin{array}{c|c|c|c|c}m&\lambda&L&d&y\\1&2\ \text{m}&3\ \text{m}&3\ \text{m}&2\ \text{m}\\1&2\ \text{m}&6\ \text{m}&3\ \text{m}&4\ \text{m}\\1&2\ \text{m}&9\ \text{m}&3\ \text{m}&6\ \text{m}\\\end{array}

The diagram contrast matches both sweeps

The top checked case uses third order at the original screen distance. The lower checked case uses first order at the longer screen distance. The table and diagram therefore tell the same scaling story.

m=3\Rightarrow y=12\ \text{m};\qquad L=9\ \text{m}\Rightarrow y=6\ \text{m}