Q1. Light of wavelength 500 nm falls on two slits 0.2 mm apart. Find the fringe width on a screen 1 m away.
β = λD/d
β = (500×10⁻⁹ × 1) / (0.2×10⁻³)
β = 5×10⁻⁷ / 2×10⁻⁴ = 2.5×10⁻³ m = 2.5 mm
Wave Optics — Class 12
Light is a wave — and waves interfere. Learn Young's experiment and diffraction, and compute the fringe width for any set-up.
Huygens' principleEvery point on a wavefront acts as a source of secondary wavelets; their common tangent gives the new wavefront.
Interference & coherenceTwo coherent waves (constant phase difference) superpose to give bright fringes (constructive) and dark fringes (destructive).
Young's double slitTwo slits produce equally spaced bright and dark fringes. Fringe width β = λD/d (D = screen distance, d = slit separation).
DiffractionThe bending/spreading of light around edges or a single slit, giving a wide central maximum with minima at a·sinθ = nλ.
Fringe-width calculator Interactive
Set the wavelength, screen distance and slit separation to find the fringe width in Young's experiment.
Fringe width, β = λD/d—mm
Fringes get wider (easier to see) with longer wavelength, a bigger screen distance, or slits placed closer together.
Numericals practice Interactive
Fringe-width problems with steps.
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Solved numericals
Q2. State two conditions for sustained interference of light.
The two sources must be COHERENT (constant phase difference).
They should have the same frequency and nearly equal amplitude, and be narrow and close together.
Formula sheet
| Quantity | Formula | SI unit |
|---|---|---|
| Fringe width | β = λ D / d | metre (m) |
| Constructive interference | path diff = n λ | — |
| Destructive interference | path diff = (n + ½) λ | — |
| Single-slit minima | a sinθ = n λ | — |
Common mistakes & exam wins
- Fringe width β = λD/d — widen the fringes by increasing λ or D, or decreasing d.
- Interference needs COHERENT sources (from a single source split in two, as in Young's experiment).
- In diffraction the central maximum is twice as wide and much brighter than the side maxima.
- Bright fringe ⇒ path difference = nλ; dark fringe ⇒ (n + ½)λ.
Frequently asked questions
What is the fringe width in Young's double-slit experiment?
The distance between two consecutive bright (or dark) fringes, β = λD/d, where D is the screen distance and d the slit separation.
What is the difference between interference and diffraction?
Interference is superposition of waves from two (or more) coherent sources; diffraction is the bending/spreading of a wave from a single slit or edge.
What are coherent sources?
Two sources that emit waves of the same frequency with a constant phase difference — essential for a steady interference pattern.
What is Huygens' principle?
Every point on a wavefront is a source of secondary spherical wavelets, and the new wavefront is the forward envelope (tangent) of these wavelets.