Young's Double-Slit
Fringe width β = λD/d. Live colored interference pattern on screen.
Key Notes
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.
Formulas
Fringe Width
Spacing between consecutive bright (or dark) fringes.
Bright fringes
Constructive interference condition.
Dark fringes
Destructive interference condition.
Intensity
I₀ = intensity from a single slit. Goes 0 → 4I₀ between bright and dark.
Phase difference
Conversion between path difference and phase difference.
Glass-slab shift
Extra optical path (μ−1)t shifts the whole pattern toward the slit covered.
Important Points
If the experiment is done under water (refractive index μ), every wavelength becomes λ/μ inside water, so β shrinks by a factor of μ.
If the source is moved perpendicular to the slits, the pattern shifts but β is unchanged.
If one slit is covered, the pattern becomes single-slit diffraction (broad bright central + faint side bands) — no interference fringes.
If the two slits have unequal intensities I₁ and I₂, fringes still form but with finite minimum: I_min = (√I₁ − √I₂)². Visibility V = (I_max − I_min)/(I_max + I_min) drops below 1.
Fringes are non-localized — they appear at any distance from the slits (in principle). β scales linearly with D.
The number of fringes that fit on a screen of length L is L/β. JEE often asks for the count of bright or dark fringes in a given range.
Young's Double-Slit notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.