STUCK IN PHYSICSAll simulations ↗Choose a point on the screen. Follow the two paths and see why the waves reinforce or cancel there.
Path lengths are rounded; Δr is calculated before rounding. The wavelength is in nanometres, path difference in micrometres.
Central maximum: both paths have equal length.
Click or drag on the curve to move point P. The dashed line marks its screen position. The screen runs from −15 mm to +15 mm.
These maximum/minimum conditions apply to each wavelength separately. White light has no single wavelength.
At a maximum, the waves arrive in phase: the path difference is a whole number of wavelengths.
At a minimum, they arrive half a cycle out of phase: the path difference is an odd number of half-wavelengths.
Intensity is shown relative to the central maximum. The path difference Δr is signed; the intensity is the same at +y and −y.
1. Increase the source separation. Do the maxima move closer together or farther apart?
2. Keep d and L fixed and increase the wavelength. What happens to the spacing?
3. Choose a maximum, then a minimum. Compare Δr/λ and the two path lengths.
4. Select a point above the centre, then the same distance below. What changes sign, and what stays the same?
Exact path lengths are used. In white-light mode, the solid graph adds the intensities of different wavelengths; the dashed curve shows the selected reference colour.
At the centre, Δr = 0 for every wavelength: all colours reach a maximum together. Away from the centre, maxima for different colours occur at different positions. Coloured fringes appear close to the middle, then overlap and lose contrast farther out. Without a diffraction envelope, the far-screen intensity approaches half the central maximum rather than disappearing.
A minimum for the selected colour does not cancel all of white light. The white-light graph therefore need not reach zero where the dashed single-colour curve does.
Two coherent copies of the same illumination reach a screen. Each wavelength interferes only with its matching wavelength from the other source. Different wavelengths are mutually incoherent, so their time-averaged intensities add.
Single-colour light covers 380–750 nm. White light uses equal spectral power over that range, sampled at 1 nm. The graph shows total relative radiant intensity, normalised to the central maximum. Approximate CIE colour matching and sRGB conversion provide illustrative screen colours; the white spectrum is white-balanced at the centre. Colours and perceived brightness are display-dependent.
The sketch magnifies source separation and wavefront spacing independently; it is not to scale. White-mode wavefronts show only three representative colours, while the screen and total graph use the full sampled spectrum. The coloured paths identify S₁ and S₂ and do not represent different source wavelengths. The model assumes equal amplitudes at the screen and omits geometric spreading, slit diffraction and spectral variation in detector response.
References: White-light interference (Ohio State); CIE colour approximation (Wyman, Sloan and Shirley).
Change the source separation, wavelength and screen distance. Select a point to compare the two paths, path difference and the linked intensity–position graph. Switch to white light to see the combined spectrum and inspect an individual reference colour.
Supports wave-interference topics in IB Physics, A Level Physics and AP Physics 2. Path lengths use the exact geometry, and the diagram enlarges source separation and wavefront spacing for clarity.