Formula & Calculator
Double-Slit Interference Fringe Spacing
Calculates the spacing between bright fringes in a double-slit interference pattern.
Interpretation
Δy = λL/d. Distance between adjacent bright fringes in Young's experiment. Used to measure wavelength and slit spacing.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| Δy | Fringe spacing | m |
| λ | Wavelength of light | m |
| L | Distance to screen | m |
| d | Slit separation | m |
What it means
The fringe spacing in Young’s double‑slit experiment is constant and given by the formula. It is used to measure the wavelength of light and to calibrate optical systems. The formula is derived from the interference condition. Understanding this is essential for wave optics and for interpreting interference patterns. It also applies to grating interference. The spacing increases with wavelength and distance to the screen and decreases with slit separation.
Worked example
Double‑Slit Fringe Spacing – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| λ (nm) | 632.8 |
| L (m) | 2 |
| d (mm) | 0.5 |
| Parameter | Value |
|---|---|
| λ | 532 |
| L | 1.5 |
| d | 0.3 |
Common mistakes
- Double‑slit fringe spacing: Δy = λ·L / d – the distance between adjacent bright (or dark) fringes.
- λ: Wavelength of light – in metres.
- L: Distance from slits to screen – in metres.
- d: Slit separation – in metres.
- Units: Δy in metres – consistent with L and d.
- Assumes: Small angles (sinθ ≈ tanθ).
Applications
Double‑slit interference fringe spacing, Δy = λ·L/d, gives the distance between adjacent bright (or dark) fringes in Young's experiment, where λ is wavelength, L is distance to screen, and d is slit separation. This formula is used in wave optics to measure wavelength, to characterise light sources, and to design interference‑based sensors. Engineers use it in optical metrology for displacement and surface profiling. By measuring fringe spacing, they can determine the wavelength of light or the slit separation. This equation is also used in holography and in testing optical components. Understanding interference fringe spacing is essential for many precision measurement applications.
- Wavelength measurement using Young's experiment
- Optical metrology for displacement and strain
- Interferometer design and calibration
- Testing optical surfaces and coatings
- Education on wave interference
Frequently Asked Questions
It calculates the spacing between adjacent bright (or dark) fringes in a double‑slit interference pattern: Δy = λL/d.
Δy = fringe spacing (distance between adjacent maxima).
λ = wavelength of light.
L = distance from slits to screen.
d = slit separation.
From the condition for constructive interference: d sinθ = mλ. For small angles, sinθ ≈ y/L, so Δy = λL/d.
Δy doubles because Δy ∝ λ.
Δy is inversely proportional to d; increasing d makes the fringes closer together.
d = 0.5 mm, L = 2.0 m, λ = 600 nm. Δy = (600×10⁻⁹ × 2.0) / (0.5×10⁻³) = 2.4×10⁻³ m = 2.4 mm.
- Confusing fringe spacing with the position of a specific fringe (y_m).
- Forgetting that the formula applies to small angles; for large angles, use the exact expression.
- Not converting units to metres.
In a medium of index n, the wavelength becomes λ/n, so Δy decreases by a factor of n.
They are often used interchangeably; fringe width is the distance between successive maxima or minima, i.e., Δy.
By measuring Δy, L, and d, one can calculate λ = Δy·d/L.