Difficulty: Intermediate | Prerequisites: Superposition, constructive/destructive interference conditions, wave properties of light
The double-slit experiment with light is one of the most important demonstrations in physics. It proved that light behaves as a wave by showing interference fringes on a distant screen. This topic takes the same path-length-difference logic from ripple-tank interference and applies it to monochromatic light passing through two narrow slits. You should already understand constructive and destructive interference conditions and be comfortable with the idea of wavelength and path difference.
Monochromatic light through two narrow slits produces alternating bright and dark fringes on a screen. Bright fringes occur where the path length difference is a whole number of wavelengths. Moving the screen closer to the slits makes the bright fringes closer together.
Bright fringe (constructive interference maximum)
A bright band on the screen where waves from the two slits arrive in phase. The path length difference is an integer multiple of the wavelength: Δr = mλ.
Think of it as the spots where the light waves help each other out.
Dark fringe (destructive interference minimum)
A dark band on the screen where waves from the two slits arrive half a cycle out of step. Δr = (m + 1/2)λ.
These are the spots where the light waves cancel.
Central maximum
The bright fringe at the centre of the screen, directly opposite the midpoint of the two slits. Here Δr = 0, so the waves always arrive in phase regardless of wavelength.
Fringe spacing
The distance between adjacent bright fringes on the screen. It depends on the wavelength, slit separation, and the distance from the slits to the screen.
Slit separation (d)
The distance between the centres of the two slits. A larger d produces more closely spaced fringes.
The pattern on the screen shows alternating bright and dark bands, symmetric about the central maximum.
The central maximum (centre of the screen) corresponds to Δr = 0.
Each bright fringe outward from the centre corresponds to the next integer multiple of λ: the first bright fringe has Δr = λ, the second has Δr = 2λ, and so on.
Dark fringes sit between the bright ones, at Δr = λ/2, 3λ/2, 5λ/2, and so on.
Count the number of bright fringes from the centre of the screen to the point in question.
If the point sits on a bright fringe, Δr equals that count times λ.
If the point sits on a dark fringe, Δr equals that count times λ plus λ/2.
Example: if a point X sits on the third bright fringe from the centre on one side, Δr = 3λ.
The angular positions of the fringes are set by the slit separation and wavelength. They do not change when the screen moves.
Moving the screen closer to the slits reduces the distance over which those angles spread out, so the bright fringes move closer together on the screen.
Moving the screen farther away makes the fringes spread out more.
The number of fringes does not change, only their physical spacing on the screen.
Condition for bright fringes (constructive):
d \sin\theta = m\lambda \quad (m = 0, \pm1, \pm2, \ldots)Condition for dark fringes (destructive):
d \sin\theta = \left(m + \tfrac{1}{2}\right)\lambdaFringe spacing on a distant screen (small angle approximation):
\Delta y = \frac{\lambda L}{d}where L is the distance from slits to screen, d is the slit separation, and Δy is the spacing between adjacent bright fringes.
Double-slit interference is the principle behind optical interferometry, used in precision measurements of distance, surface flatness, and even gravitational waves (LIGO). Anti-reflective coatings on camera lenses and glasses use thin-film interference, which works on the same path-difference logic as double-slit fringes.
Students often think that moving the screen closer changes the number of fringes. It does not. It changes only the physical spacing between them on the screen.
A common error is confusing fringe order with the number of bright bands visible. The order (m) refers to how many wavelengths of path difference exist, not the total count of fringes.
Students sometimes assume a point halfway between two bright fringes must be "partially bright." It is actually a dark fringe (destructive interference minimum).
Students may mix up the effect of changing slit separation with changing screen distance. Increasing d makes fringes closer together; decreasing L also makes them closer together. These are independent effects.
⚠️ You will likely be given a diagram of fringes and asked to determine Δr at a marked point. Count bright fringes from the centre.
⚠️ Questions about moving the screen closer or farther are common. The answer is always about fringe spacing, not fringe count.
⚠️ Know the fringe spacing formula Δy = λL/d. If any one of the three variables changes, you should be able to say how the spacing responds.
True or false: The central maximum of a double-slit pattern always has Δr = 0. (True.)
Fill in the blank: The third bright fringe from the centre has a path length difference of ____. (3λ.)
True or false: Moving the screen farther from the slits makes the bright fringes closer together. (False: they spread farther apart.)
Fill in the blank: If d is doubled while λ and L stay the same, fringe spacing is ____. (Halved.)
Q: A double-slit experiment produces bright and dark fringes on a distant screen. Point X sits on the third bright fringe from the centre. What is Δr at point X?
A: Δr = 3λ. Each bright fringe outward from the centre adds one wavelength of path difference.
Q: The screen is moved closer to the mask with the two slits. How does the fringe pattern change?
A: The bright fringes move closer together on the screen. The fringe spacing is proportional to L (the slit-to-screen distance), so reducing L reduces the spacing. The number of fringes and their angular positions remain unchanged.
Q: If you replaced the light source with one of shorter wavelength, what would happen to the fringe pattern?
A: The fringes would be closer together. Fringe spacing Δy = λL/d, so a shorter λ gives a smaller Δy.
Double-slit interference connects directly to single-slit diffraction, which explains the overall intensity envelope within which the double-slit fringes sit. It also connects to diffraction gratings, which are essentially many slits and produce sharper, more widely spaced bright fringes. The underlying wave model of light is what makes hydrogen emission spectra observable through a spectrometer.
Double-slit experiment, Young's double slit, two-slit interference, bright fringe, dark fringe, fringe spacing, central maximum, path length difference, Δr, slit separation, monochromatic light, interference pattern on screen, PHYS 116A, UW Physics 116A, wave optics, Δy = λL/d