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Concept module

Double-Slit Interference

Use two coherent slits and one screen to connect path difference, phase difference, and fringe spacing to wavelength, slit separation, and screen distance on one compact optics bench.

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Starter track

Step 3 of 50 / 5 complete

Wave Optics

Earlier steps still set up Double-Slit Interference.

1. Polarization2. Diffraction3. Double-Slit Interference4. Dispersion / Refractive Index and Color+1 more steps

Previous step: Diffraction.

Start from track beginning

Why it behaves this way

Explanation

Double-slit interference is the optics version of a wave-interference idea you have already seen: two coherent arrivals reach the same place, and their path difference sets whether they reinforce or cancel. Here the two arrivals come from two narrow slits and land on one screen.

This bench keeps the model intentionally bounded: one wavelength, one slit separation, one screen distance, and one movable probe on the screen. The same geometry drives the stage, the pattern graph, prediction mode, worked examples, and challenge checks so the fringe pattern stays tied to one honest optics story instead of a giant wave-optics engine.

Key ideas

01A screen point is bright when the path difference is close to a whole-number multiple of the wavelength, and dark when it is close to a half-number multiple.
02The path difference becomes a phase difference through \(\Delta \phi = 2\pi \Delta r / \lambda\), so wavelength controls how much phase each extra meter contributes.
03For small angles, the bright-fringe spacing is approximately \(\Delta y \approx \lambda L / d\), so larger wavelength or screen distance widens the fringes while larger slit separation tightens them.
04This page extends Wave Interference and Diffraction into optics without pretending to simulate every detail of full wave propagation.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough
These examples read the live geometry directly from the current optics bench, so the algebra stays attached to the same fringe pattern you are looking at.

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Frozen valuesUsing frozen parameters

For the current probe position at y = 0.8, what phase split reaches that screen point?

Probe height

0.8 m

Path difference

0.37 m

Wavelength

0.78 m

1. Start from the interference relation

Use .

2. Substitute the live geometry

.

3. Wrap the comparison angle

That path difference is about 0.48 wavelengths of extra travel, so the wrapped phase comparison is 2.99 rad.

Current phase split

The path difference is close to half a wavelength, so the slit contributions arrive nearly opposite in phase and the probe sits on a dark fringe.

Fringe-spacing checkpoint

You want the fringes farther apart on the same screen. Which control changes are reliable and which one is only sampling a different point?

Make a prediction before you reveal the next step.

Decide whether changing wavelength, slit separation, screen distance, or probe height actually widens the fringe spacing.

Check your reasoning against the live bench.

Increase wavelength, increase screen distance, or decrease slit separation. Probe height only samples a different place on the existing pattern.
Fringe spacing follows the geometry rule \(\Delta y \approx \lambda L / d\). The probe does not create the pattern; it only reads one location on it.

Common misconception

A dark fringe means the light from one slit did not reach that point on the screen.

Both slits still feed the same screen point. The dark fringe appears because the two coherent contributions arrive with nearly opposite phase.

The screen pattern is set by superposition, not by one slit turning off at selected places.

Quick test

Reasoning

Question 1 of 4

Answer from path difference, phase, and geometry together rather than treating the pattern as a memorized slogan.

Which condition best describes a bright fringe in this double-slit bench?

Use the live bench to test the result before moving on.

Accessibility

The simulation shows incoming wavefronts striking a barrier with two narrow slits. On the right, a vertical screen strip brightens and darkens to show the interference pattern, and a movable probe marks one selected screen height.

Optional overlays show the slit geometry, the two slit-to-probe paths, approximate fringe-spacing markers, and a phase wheel that compares the two slit contributions at the current probe point.

Graph summary

The probe-field graph shows the two slit contributions and their live resultant at one selected screen point as functions of time.

The screen-pattern graph shows relative intensity against screen height, so it stays position-based even while the time rail continues to inspect the local probe field.