The double-slit experiment conducted by Thomas Young in 1801 decisively demonstrated the wave nature of light. We will learn how to find the wavelength of light from the spacing of bright and dark fringes.
Basic Knowledge
Young’s double-slit experiment:
When the slit separation is d and the distance from the slits to the screen is L (L >> d), interference fringes appear on the screen.
Approximate path difference at a position y from the center of the screen: Δ ≈ dy/L
・Condition for bright fringes (constructive interference): dy/L = mλ → ym = mλL/d（m = 0, ±1, ±2, …）
・Condition for dark fringes (destructive interference): dy/L = (m + 1/2)λ → ym = (m + 1/2)λL/d
Spacing of bright fringes（distance between adjacent bright fringes）: Δy = λL/d
Using this: λ = Δy × d / L（experimental determination of wavelength）
Double-slit experiment (Young’s experiment)（Fringes are produced on a screen by interference of light from two parallel slits）
Interference-fringe spacing Δy = λL/d（Determined by the wavelength, slit separation, and screen distance）
Coherent light sources（To produce interference fringes, the two slits must emit waves in phase. Usually, light diffracted by a single slit is used）
Bright fringes / Dark fringes（Locations of constructive interference / Locations of destructive interference）
Measurement of wavelength（From Δy = λL/d, λ = Δy × d/L）
Further Study (Background・Significance)
Young’s experiment was a historic experiment that settled the conflict between the wave theory of light (Fresnel and Young) and Newton’s corpuscular theory.
Today, it has been confirmed that interference fringes appear even when single photons or electrons pass through a double slit one at a time, demonstrating the essence of wave-particle duality in quantum mechanics (when we observe “which slit an individual electron passes through,” the interference fringes disappear).
From Δy = λL/d: making d smaller (bringing the slits closer together) and L larger (using a more distant screen) widens the fringe spacing and makes observation easier. In practice, laser light is used to ensure coherence.
- Bright-fringe spacing Δy = λL/d（calculate wavelength from 3 quantities）
- Bright-fringe condition: dy/L = mλ（m-th bright fringe）
- Dark-fringe condition: dy/L = (m+1/2)λ
- Determine the wavelength experimentally using λ = Δy × d/L
- Making d smaller and L larger widens the fringes
Points to Note (Easily Confused)
① In Δy = λL/d, d is the “slit separation” (not the slit width). ② The formula holds under the approximation L >> d. Check the problem statement. ③ The y-coordinate of the m-th bright fringe is ym = mλL/d (m = 0 is the central bright fringe). ④ Light does not “disappear” at dark fringes; energy is redistributed to other bright fringes (conservation of energy).
Practice
- When the slit separation is d = 0.50 mm and the distance to the screen is L = 2.0 m, the bright-fringe spacing is 2.0 mm. Find the wavelength of the light.
- Under the conditions above, what happens to the bright-fringe spacing when the slit separation is doubled?
- Interference fringes were observed on the screen in Young’s experiment. What property of light does this provide evidence for? Also explain why it provides that evidence.