Young’s Double Slit: Wavelength
Double-slit fringes at a known screen distance. Measure the fringe spacing at several slit separations and recover the hidden λ from a fit of Δy versus 1/d.
Goal
Determine λ from Δy = λ L / d (small angles). The slope of Δy (mm) versus 1/d (1/µm) equals λ L when λ is in nm and L in metres.
Equipment
- Double slit
- Screen at known L
- Travelling microscope (Δy)
Experiment
Theory
Bright fringes sit at d sinθ = m λ. On a distant screen y ≈ L tanθ ≈ L sinθ, so the spacing is Δy ≈ λ L / d. The bench hides λ and the first-maximum angle; you only read a millimetre scale after each measurement.
Procedure
- Screen distance L is fixed and known. Wavelength is hidden. Double-slit mode only.
- Set the slit separation d and record. The travelling microscope logs Δy with small noise. There is no live Δy while you drag d.
- The notebook computes 1/d. Repeat for at least 6 values of d from about 150 µm to 500 µm (0.15–0.50 mm).
- Fit Δy (mm) versus 1/d (µm⁻¹); λ (nm) = slope / L. Compare with the reference.
Conclusion
The fitted wavelength agrees with the hidden λ. Main uncertainties: microscope noise, the small-angle approximation, and treating the envelope as not shifting the fringe pitch.