young-fringe-position-cites-the-path-source

In Young's double-slit, the m-th bright fringe sits at y_m = m * lambda * L / d, where d is the slit spacing and L the screen distance. The formula comes straight from the path-difference condition, delta = m * lambda, paired with the small-angle approximation. The exact position holds only for coherent monochromatic light, a known wavelength, and aligned slits; real fringes blur with bandwidth, finite slit width, screen calibration, and detector noise.

The paraxial screen position is source-bound to a checked bright path difference. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The screen row starts from a bright path source

The Young-fringe helper does not invent a screen position by itself. It cites an accepted bright path-difference source, then uses the slit spacing and screen distance.

\text{path source accepted}=1

Fringe position scales with order

Hold wavelength, screen distance, and slit spacing fixed. The screen position grows in the same ratio as the order.

\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}

The first Young fringe cites a path source

The fringe position is accepted only after the Young check cites the bright path-difference source.

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