0.126051
2.2
mm
2.2
mm
549.778
nm
454
0.0002
%
0.126051
2.2
mm
2.2
mm
549.778
nm
454
0.0002
%
The Double Slit Interference Calculator solves Young's double-slit equation d sin θ = mλ for bright fringe positions, wavelength, or slit separation. It computes fringe spacing, the position of any bright fringe on a screen, and the path difference between the two interfering beams — the essential quantities for understanding one of the most famous experiments in physics.
Young's double-slit experiment, first performed in 1801, provided definitive evidence for the wave nature of light. By sending monochromatic light through two closely spaced slits, Thomas Young observed a pattern of alternating bright and dark bands that could only be explained by wave interference. Today the experiment remains a cornerstone of physics, illustrating interference for light, electrons, neutrons, and even large molecules.
Two narrow slits separated by distance d are illuminated by coherent light of wavelength λ. At the observation screen (distance L away), constructive interference (bright fringes) occurs when the path difference from the two slits is a whole number of wavelengths:
$$d\sin\theta = m\lambda, \quad m = 0, \pm1, \pm2, \ldots$$
Destructive interference (dark fringes) occurs at half-integer orders:
$$d\sin\theta = \left(m + \tfrac{1}{2}\right)\lambda$$
For small angles (θ << 1 radian), sin θ ≈ tan θ ≈ y/L, where y is the distance from the central maximum on the screen. The position of the m-th bright fringe is:
$$y_m = \frac{m\lambda L}{d}$$
The fringe spacing — the distance between adjacent bright fringes — is constant in the small-angle approximation:
$$\Delta y = \frac{\lambda L}{d}$$
This formula shows that fringe spacing increases with wavelength and screen distance but decreases with slit separation. The intensity at any point follows:
$$I = 4I_0\cos^2\left(\frac{\pi d \sin\theta}{\lambda}\right)$$
where I₀ is the single-slit intensity. The maximum observable order is limited by the geometric condition sin θ ≤ 1, giving m_max = floor(d/λ).
The fringe spacing Δy gives the distance between consecutive bright bands on the screen. Larger spacing means the fringes are more spread out and easier to observe. If Δy is very small (say, less than 0.1 mm), the fringes may be too fine to resolve with the naked eye. The path difference column confirms the interference condition — it should be an integer multiple of the wavelength for bright fringes. The maximum order tells you how many bright fringes exist on each side of the central maximum.
Inputs
Results
With 0.25 mm slit separation and 550 nm light, first-order bright fringes appear at ±0.126°. On a screen 1 m away, the fringe spacing is 2.2 mm — easily visible with the naked eye. This is a typical undergraduate lab setup.
Inputs
Results
If the third-order bright fringe appears at 0.473° with d = 0.20 mm, the wavelength is about 550 nm — in the green part of the visible spectrum.
Young's experiment sends coherent light through two narrow, closely spaced slits. The light from each slit interferes on a distant screen, producing a pattern of alternating bright and dark bands (fringes). The bright fringes occur where the two beams arrive in phase (constructive interference) and dark fringes where they are half a wavelength out of phase (destructive interference).
Coherent light maintains a constant phase relationship between the two slits. Incoherent sources (like an ordinary light bulb) have random phase fluctuations that wash out the interference pattern. In practice, coherence is achieved using a laser or by first passing light through a single narrow slit before the double slit.
Fringe spacing Δy = λL/d depends on three factors: it increases with wavelength (red fringes are wider than blue), increases with screen distance L, and decreases with slit separation d. This makes fringe spacing a direct measure of wavelength.
Yes. In 1961, Claus Jönsson demonstrated double-slit interference with electrons, confirming their wave nature. Even when electrons are sent one at a time, an interference pattern builds up, illustrating wave-particle duality and the probabilistic nature of quantum mechanics.
Interference arises from the superposition of waves from distinct sources (the two slits). Diffraction arises from a single aperture. In a real double-slit experiment both occur simultaneously: interference creates the fine fringe pattern while single-slit diffraction creates a broad envelope that modulates the fringe intensities.
Each slit has finite width, producing a single-slit diffraction envelope that decreases in intensity at larger angles. The double-slit interference fringes are multiplied by this envelope, so higher-order fringes (at larger angles) appear progressively fainter. Some orders may even be missing if they coincide with a diffraction minimum.
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