💡 Interference & diffraction
Young's double slit: Fringe width β = λD/d. Bright fringe position y_n = nλD/d; dark y_n = (2n−1)λD/(2d). Diffraction grating: d sin θ = n λ (d = grating spacing). Single slit: Angular width of central maximum ≈ 2λ/a (a = slit width).
Wave optics calculators
Young, grating, single slit
Wavelength λ
Screen distance D
Slit separation d
Fringe width β = λD/d
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Wavelength λ
D
Slit separation d
Fringe order n
Type
Position y from centre
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Solve for
Grating element d
Order n
Wavelength λ
Angle θ (°)
d sin θ = n λ
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Wavelength λ
Slit width a
Angular width ≈ 2λ/a
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〰️ Diagram
🧮Step-by-Step Solution▼ Show
| Concept | Formula | Notes |
|---|---|---|
| Path difference (bright) | Δx = n λ | Constructive |
| Path difference (dark) | Δx = (2n+1) λ/2 | Destructive |
| Fringe width (Young) | β = λ D / d | D = screen distance, d = slit separation |
| Diffraction grating | d sin θ = n λ | d = grating element |
| Single slit (angular width) | ≈ 2λ/a | a = slit width |
About wave optics
In Young's double slit, constructive interference occurs when path difference Δx = nλ, giving bright fringes. Fringe width β = λD/d. Position of nth bright fringe from centre: y_n = nλD/d; nth dark: y_n = (2n−1)λD/(2d). A diffraction grating with slit spacing d gives maxima at d sin θ = n λ. For a single slit of width a, the angular width of the central maximum (between first minima) is approximately 2λ/a.