The experiment that showed light is a wave
Around 1801, the English physician and physicist Thomas Young let sunlight pass through two narrow openings close together and observed a series of bright and dark bands on a screen. Particles would have made two bright stripes. The bands, called interference fringes, can only be explained if light behaves as a wave: the waves from the two slits reinforce each other where they arrive in step and cancel where one arrives a half wavelength behind the other.
The formulas
Bright fringes appear at angles where the path difference is a whole number of wavelengths:
d sin θ = m λ
On a distant screen, the bright fringes are evenly spaced by
Δy = λ L ÷ d
- λ is the wavelength of the light.
- d is the distance between the centers of the two slits.
- L is the distance from the slits to the screen.
- m is the order of the fringe: 0 for the central fringe, 1 for the next, and so on.
Each slit, being of finite width a, also spreads the light by diffraction. The central diffraction maximum has a width of about 2λL ÷ a, and the interference fringes are visible inside it.
Worked example
A green laser pointer (532 nm) shines on two slits 0.25 mm apart, each 0.05 mm wide, with a screen 6 ft (1.83 m) away:
- Fringe spacing: 532 × 10⁻⁹ × 1.83 ÷ 0.00025 = 3.89 mm.
- The first-order bright fringe sits at an angle of 0.122°, 3.89 mm from the center.
- The central diffraction maximum is 38.9 mm wide.
- Because d is exactly 5 times a, the 5th-order fringes fall on diffraction minima and vanish, leaving 9 bright fringes in the central maximum.
Doing the experiment at home
Cover a microscope slide with soot or paint, and scratch two lines close together with two razor blades held side by side. Shine a laser pointer through the scratches onto a wall a few yards away. Never look into the laser beam or at its reflection from a mirror.
Beyond light
Electrons, neutrons, atoms and even molecules of 2,000 atoms have produced double-slit patterns, even when sent one at a time. Each particle lands at a single point, but the pattern builds up as if each one passed through both slits. Richard Feynman called this experiment the one that holds “the only mystery” of quantum mechanics.
Accuracy
The evenly spaced formula assumes small angles, where tan θ ≈ sin θ. The calculator uses the exact angle for the position of the chosen fringe, so it stays accurate for fine slits and high orders.