Young's Double-Slit

Coherent monochromatic light incident on two narrow parallel slits S₁ and S₂ produces alternating bright and dark fringes on a distant screen — Young's classic 1801 experiment.

Path difference at a point P on the screen: Δ = d sin θ ≈ dy/D, where d = slit separation, D = slit-to-screen distance, y = distance from central axis.

Bright fringes (constructive): Δ = nλ. Dark fringes (destructive): Δ = (n + ½)λ.

Fringe width β = λD/d. β depends only on the wavelength, geometry, and is the same for all orders.

Intensity on the screen: I(θ) = 4I₀ cos²(πd sin θ / λ). All bright fringes have equal intensity in this idealization (ignoring diffraction envelope).

Central bright fringe is at the screen point equidistant from both slits — i.e., the perpendicular bisector of the two slits hits the screen.

Inserting a thin glass slab in front of one slit shifts the fringe pattern by a distance (μ − 1)t·D/d toward that slit, where μ is the slab's refractive index.