Interference of Light
Simple Explanation
When light from two coherent sources (like two narrow slits) overlaps, it produces a pattern of bright and dark fringes — bright where the waves arrive in step (constructive interference) and dark where they arrive out of step (destructive interference). The spacing between bright fringes is Δy=λL/d.
Why Do We Need It?
Interference is direct, visible proof that light behaves as a wave — a purely particle picture of light cannot explain why two light sources can combine to produce darkness at some points.
See It
Two closely-spaced slits on the left, with light spreading out from each toward a screen on the right, where alternating bright and dark fringes are marked
Formula
Double-Slit Fringe Spacing
Δy = λL/d
In a double-slit interference pattern, the spacing between adjacent bright fringes on the screen depends on the wavelength of light, the distance to the screen, and how far apart the two slits are.
- Δy
- — spacing between adjacent bright fringes, in metres (m)
- λ
- — wavelength of the light, in metres (m)
- L
- — distance from the slits to the screen, in metres (m)
- d
- — distance between the two slits, in metres (m)
When to use it: Whenever the spacing between bright fringes in a double-slit interference pattern needs to be found — or used to work backward to find the light's wavelength.
Worked Example
Find the fringe spacing in a double-slit experiment
Light of wavelength 600 nm passes through two slits 0.5 mm apart, forming a pattern on a screen 2 m away. Find the spacing between adjacent bright fringes.
Why Does This Work?
At a bright fringe, light from the two slits has traveled paths differing by a whole number of wavelengths, so the waves arrive crest-to-crest (constructive interference); moving along the screen changes that path difference smoothly, producing evenly-spaced bright fringes exactly Δy=λL/d apart.
Real-Life Example
Thomas Young's original double-slit experiment
In 1801, Thomas Young shone light through two narrow slits and observed a striped pattern on a screen, rather than just two bright lines.
This striped interference pattern was the first strong evidence that light behaves as a wave — a discovery that directly launched the wave theory of light still used today.
Practice
Light of wavelength 500 nm passes through two slits 0.3 mm apart, forming a pattern on a screen 1.5 m away. Find the fringe spacing, in mm.
HardCommon mistake
Mixing units — forgetting to convert nanometres, millimetres, and metres into one consistent unit before substituting into the formula is one of the most common sources of a wrong answer here.
Quick Review
- Δy = λL/d.
- Bright fringes: constructive interference (waves in step). Dark fringes: destructive (out of step).
- Direct evidence that light behaves as a wave.