Double-Slit Lab: Measuring the Fringe Spacing
The same wave engine as the ripple tank, dedicated to one experiment. The slit-separation slider physically moves the slits in the barrier; the D slider physically moves a detector line through the tank; the frequency slider is your wavelength dial (λ = v/f). A detector integrates the real wave field along the screen line, marks the bright fringes it finds, and measures the fringe spacing — shown beside the exact wave-theory value and the x = λD/a prediction, so students see both the formula working and its far-field small print.
Same tank, same physics as the ripple tank — dedicated to one experiment. Brass = the double-slit barrier (the a slider moves the slits). Dashed green line = the detector screen (the D slider moves it). The brass profile on its right is the integrated wave intensity — its red dots are the bright fringes the sim itself detects.
Three numbers, one story: the formula x = λD/a is a far-field approximation; the exact row solves the true path-difference geometry (no approximation); and the measured row is read off the actual wave field. Measured should track the exact theory closely — the gap to the formula is its small print, made visible.
1. Watch the slits move as you slide a — then halve a and see the fringes spread to double the spacing. Inversely related.
2. Slide the screen out with D and watch the same fringes fan out wider: x grows in proportion to D.
3. Raise f: shorter λ, tighter fringes. Rearranged, λ = xa/D — this experiment is a way to MEASURE a wavelength.
4. x = λD/a assumes D is much bigger than a. Set a = 20 cm and D = 15 cm: the formula drifts far from the exact and measured rows, which stay together. Restore D ≫ a and all three converge. Formulas have small print; this tank is small enough to show you where it is.
What Each Variable Means
Fringe spacing. Distance between adjacent lines of biggest ripples on the screen. Measured live from the detector, in cm.
Wavelength. Of the water waves: λ = v/f, with v = 30 cm/s fixed by the water. The frequency slider is your wavelength dial.
Slit-to-screen distance. From the barrier to the dashed detector line. Bigger D spreads the fringes out.
Slit separation. Between the centres of the two slits. Smaller a gives WIDER fringes — they are inversely related.