Young's Double-Slit Experiment
Coherent light through two slits paints bright and dark interference fringes.
About this simulation
Coherent light passes through two narrow slits; each slit becomes a fresh source of waves. Where crest meets crest the light adds, where crest meets trough it cancels — producing the fringe pattern on the screen. Students can vary the slit separation d, screen distance D, wavelength λ and slit width a, and watch the pattern reshape in real time. The intensity is the full Fraunhofer form — two-slit interference under the single-slit envelope — so missing orders appear where they should; see the accuracy note for where the model holds and where it stops.
How to use it
- The opening animation sweeps d, D and λ by itself; touch any control to take over, then read β above the screen: at the default settings it is 3.12 mm, the gap marked by the small bracket beside the screen.
- Drag the Slit separation slider up and watch the fringes crowd together; drag it down and they spread out, because β is inversely proportional to d.
- Move the Screen distance slider from 0.5 m towards 3 m and see the whole pattern stretch along the fixed screen, with β above it growing as D does.
- Sweep the Wavelength slider from violet to red, or tap the Red light preset under Try, and watch β grow with λ.
- Increase the Slit width slider, or tap Wide slits, and watch the dashed single-slit envelope close in so fewer fringes survive inside it.
What to notice
- The bright fringes are equally spaced, and their spacing depends only on λ, D and d, not on the slit width.
- The fringes are not equally bright: they sit under the dashed single-slit envelope, which is why they fade towards the edges of the screen.
- The count above the screen, 'fringes in the envelope', is the bright fringes inside the central diffraction maximum; it falls as the slit width a approaches the separation d.
- When d is an exact multiple of a, a bright fringe lands on a zero of the envelope and disappears: a missing order.
The formulas
- β = λD / d
- Fringe width β equals wavelength λ times slit-to-screen distance D, divided by the slit separation d.
- d sin θ = mλ
- Bright fringe of order m appears where the path difference from the two slits is a whole number m of wavelengths.
- I(θ) ∝ cos²(π d sin θ / λ) · [sin(π a sin θ / λ) / (π a sin θ / λ)]²
- Intensity is two-slit interference (first factor) multiplied by the diffraction envelope of one slit of width a (second factor).
Questions
Why does fringe width increase with wavelength in Young's double slit experiment?
A bright fringe appears where the path difference d sin θ equals a whole number of wavelengths. A longer wavelength needs a bigger angle to make the same path difference, so neighbouring bright fringes sit further apart. That gives β = λD/d, directly proportional to λ. In the simulation, change the Wavelength from 520 nm to 700 nm and β above the screen rises from 3.12 mm to 4.20 mm.
What happens to the fringes when the distance between the slits is increased?
The fringe width β = λD/d is inversely proportional to the slit separation d, so increasing d brings the fringes closer together, and the pattern becomes harder to see. Halving d doubles β. In the simulation, doubling d from 0.25 mm to 0.50 mm halves β above the screen from 3.12 mm to 1.56 mm, and more fringes fit inside the same envelope.
What is a missing order in the double slit pattern?
Each slit has a finite width a, so the whole pattern is shaped by a single-slit envelope with zeros at a sin θ = λ, 2λ and so on. If an interference maximum (d sin θ = mλ) falls exactly on one of these zeros, that bright fringe has no light to show and vanishes. This happens when d/a is a whole number. In the simulation, set d = 0.25 mm and a = 0.05 mm: orders ±5 go missing.
Why do fringes become fainter away from the central bright fringe?
Each slit diffracts light into a central lobe whose brightness falls with angle. The interference fringes are this single-slit envelope multiplied by the two-slit pattern, so the outer fringes are dimmer even though they are evenly spaced. In the simulation, the dashed curve beside the screen is that envelope, and the solid intensity profile always stays inside it.
Why must the two sources be coherent to get a stable interference pattern?
A steady pattern needs the phase difference between the two waves at each point to stay fixed in time. Two separate bulbs emit with randomly changing phases, so their bright and dark fringes shift millions of times a second and average out to uniform light. Young solved this by splitting light from a single source with two slits, which is the arrangement drawn in the simulation.
