wider-slit-spacing-pulls-young-fringes-inward - Wave Optics: Interference and Diffraction Step by Step

The same path source gives a smaller screen position when the slit spacing is larger. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Keep the source and screen distance fixed

This comparison keeps the wavelength and screen distance fixed. Only the slit separation changes.

\lambda=2\ \text{m}\qquad L=6\ \text{m}

Larger slit spacing pulls fringes inward

The denominator is the slit spacing. Doubling it cuts the fringe position in half, and doubling it again halves the position again.

\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}\\1&2\ \text{m}&6\ \text{m}&6\ \text{m}&2\ \text{m}\\1&2\ \text{m}&6\ \text{m}&12\ \text{m}&1\ \text{m}\\\end{array}

A wider slit spacing moves fringes inward

With the same wavelength and screen distance, the checked position falls when the slit separation is larger.

y=\frac{m\lambda L}{d}=\frac{1\cdot2\ \text{m}\cdot6\ \text{m}}{6\ \text{m}}=2\ \text{m}