Double-Slit Fringe Spacing
Spacing of interference fringes on a screen.
Formula
Variables
How it works
In a double-slit experiment, each bright fringe appears where the two waves travel paths that differ by one whole wavelength, so they arrive in phase and reinforce each other. For small angles on a distant screen, that path difference translates into evenly spaced bright and dark bands, and the gap between adjacent bright fringes is bbL/d. The formula shows that fringes spread out more for longer wavelengths or a farther screen, and crowd together when the slits are farther apart.
When to use it
Use this when analyzing interference patterns from two narrow slits or two coherent sources on a distant screen. It is especially useful for finding fringe spacing, slit separation, or wavelength in lab optics problems.
Worked example, step by step
A laser of wavelength 632.8 nm passes through two slits separated by 0.20 mm. The screen is 1.50 m away. Step 1: Write the formula: b4y = blL / d Step 2: Convert units: bl = 632.8 d7 10^-9 m, L = 1.50 m, d = 0.20 d7 10^-3 m Step 3: Substitute: b4y = (632.8 d7 10^-9 d7 1.50) / (0.20 d7 10^-3) Step 4: Calculate: b4y = 4.746 d7 10^-3 m Step 5: Final answer: b4y 3d 4.75 mm between adjacent bright fringes.
Common mistakes to avoid
- Forgetting to convert millimetres or nanometres into metres before substituting
- Using the slit-to-screen distance as the slit separation, or swapping L and d
- Applying the formula when the small-angle/distant-screen approximation is not valid
Did You Know?
Young's double-slit experiment proved light is a wave, and later revealed the deep strangeness of quantum mechanics.
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