Young's Double-Slit Interference

In 1801, Thomas Young demonstrated that light is a wave by passing it through two narrow slits and observing alternating bright and dark bands — an interference pattern — on a distant screen.

Setup

Two slits separated by distance $d$ are illuminated by monochromatic light of wavelength $\lambda$. A screen is placed at distance $L$ from the slits.

Path Difference

The two waves from the slits travel different distances to any point $P$ on the screen. For a point at height $y$ above the center, the path difference is approximately:

$\Delta = \frac{y d}{L}$

Bright Fringes (Constructive Interference)

Constructive interference occurs when the path difference equals a whole number of wavelengths:

$\Delta = m \lambda \quad m = 0, \pm 1, \pm 2, \ldots$

This gives bright fringe positions:

$y_m = \frac{m \lambda L}{d}$

Fringe Spacing

The distance between adjacent bright fringes is constant:

$\Delta y = \frac{\lambda L}{d}$

Example: $\lambda = 550\,\text{nm}$, $L = 1\,\text{m}$, $d = 1\,\text{mm}$:

$\Delta y = \frac{550 \times 10^{-9} \times 1}{10^{-3}} = 0.00055\,\text{m} = 0.55\,\text{mm}$

Dark Fringes (Destructive Interference)

Destructive interference occurs at half-integer path differences:

$\Delta = \left(m + \frac{1}{2}\right) \lambda$

Finding the Fringe Order

Given a measured position $y$, the nearest bright fringe order is:

$m = \text{round}\!\left(\frac{y d}{\lambda L}\right)$

Your Task

Implement the fringe spacing formula and the order-finding function. Wavelengths are in nm, distances in meters.