Wave Optics
Two coherent slits, one screen, live interference fringes. Drag λ, slit separation d and screen distance D and watch the fringe pattern breathe in real time — β = λD/d born in front of you. A movable point P reads out path difference, phase, order and intensity; toggle white light or dip the setup in water (μ) to see the fringes shrink. Exact small-angle physics with a live intensity graph and challenge mode.
Drag λ, d and D and watch β = λD/d change live. Move point P to read Δ, φ, order and intensity. Toggle white light or a water/glass medium. Try Challenge — predict the fringe width first.
5 minutes · +4 right, −1 wrong (real NEET marking) · one global leaderboard.
Fringe width β = λD/d, where λ is the wavelength of light, D is the distance from the slits to the screen, and d is the separation between the two slits. It is the distance between two consecutive bright (or two consecutive dark) fringes, and is the same for both.
A bright fringe forms where the path difference Δ = d·sinθ ≈ d·y/D equals a whole number of wavelengths: Δ = nλ (n = 0, 1, 2, …), giving constructive interference. A dark fringe forms where Δ = (n+½)λ, giving destructive interference. The phase difference is φ = 2πΔ/λ.
Inside a medium of refractive index μ the wavelength shrinks to λ/μ while the frequency stays the same. Since β = λD/d, the fringe width also decreases by the same factor μ — the fringes move closer together. For water (μ ≈ 1.33) the fringes are about 1.33 times narrower.
At the central point the path difference is zero for every wavelength, so all colours interfere constructively there and combine to give white. Away from the centre each colour has a different fringe width (β ∝ λ), so coloured fringes appear and quickly overlap and wash out at higher orders.
For two equal coherent slits the intensity is I = 4I₀cos²(φ/2), where φ = 2πΔ/λ is the phase difference. It is maximum (4I₀) at the bright fringes where φ = 2nπ, and zero at the dark fringes where φ = (2n+1)π, producing the familiar series of evenly spaced bright and dark bands.
YDSE mein fringe width β ko double karne ke liye, in mein se kaunsa change kaam karega?