Physics · Optics

Double-Slit Interference

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Wrap-up

What you learned

Recommended next: Open concept testCheck whether the core ideas are ready without leaving this concept.
Read next: Refraction / Snell's LawMove from interference geometry to boundary bending

Key takeaway

Bright and dark bands come from path difference measured in wavelengths, not from either slit switching off.
Phase difference is the path-difference story written as an angle, so half a wavelength means near-opposite phase.
Fringe spacing widens with larger wavelength or screen distance and tightens with larger slit separation.
Probe height samples one point on the pattern; it does not change the spacing of the pattern itself.

Common misconception

A dark fringe does not mean no light reaches that screen point; it means the two coherent contributions cancel there.

Both slits still send light to that screen point.

Carry interference deeper into optics

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Boundary opticsOptics

Refraction / Snell's Law

Watch one light ray cross a boundary, connect refractive index to speed change, and see Snell's law set the refracted angle, bending direction, and critical-angle limit on the same live diagram.

Critical-angle limitOptics

Total Internal Reflection

Push a ray from a higher-index medium toward a lower-index boundary, watch the critical angle emerge, and see the same live diagram hand off from ordinary refraction to full internal reflection.

Beyond wave opticsModern Physics

Photoelectric Effect

Use one compact lamp-to-metal bench to see why light frequency sets electron emission, why intensity alone fails below threshold, and how stopping potential reads the electron energy honestly.

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Reference and support

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Equation snapshotPath, phase, and spacing · Fringe spacingShow 2 equations

Keep the path-to-phase relation beside the small-angle spacing rule while you compare the probe with the whole screen pattern.

Path, phase, and spacing
$Δ ϕ = \frac{2 π Δ r}{λ}$
Path difference matters only through how many wavelengths of extra travel it represents.
Fringe spacing
$Δ y \approx \frac{λ L}{d}$
For small angles, this gives the vertical spacing between neighboring bright fringes on the screen.

Why it behaves this way

Explanation

At any point on the screen, light from the two slits has traveled slightly different distances. That path difference decides the result: if it is close to 0, 1 wavelength, 2 wavelengths, and so on, the arrivals reinforce and the point is bright. If it is close to half a wavelength, one and a half wavelengths, and so on, the arrivals are nearly opposite in phase and the point is dark.

The stripe spacing is then set by geometry. A longer wavelength or a farther screen spreads the fringes out, while a larger slit separation packs them closer together. The probe lets you inspect one screen point in detail, and the pattern graph shows all screen points at once, so both views are reading the same interference pattern.

Key ideas

01A bright fringe appears where the path difference is close to a whole-number multiple of the wavelength, and a dark fringe appears where it is close to a half-number multiple.

02Path difference becomes phase difference through $\Delta \phi = 2\pi \Delta r / \lambda$, so wavelength sets how strongly a given distance difference affects interference.

03For small angles, the fringe spacing is approximately $\Delta y \approx \lambda L / d$, so longer wavelength or larger screen distance widens the fringes while larger slit separation narrows them.

04Probe height does not change the fringe spacing. It only samples a different point on the existing pattern.

Worked examples

Live double-slit checks

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Frozen walkthrough

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Frozen walkthrough

These examples use the live wavelength, slit spacing, screen distance, and probe height from the current bench, so each step explains the exact pattern you are viewing.

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Example 1 of 2

Frozen valuesUsing frozen parameters

At the current probe position at y = 0, what phase difference do the two slit contributions have when they reach that screen point?

y_{p}

Probe height

0 m

Δ r

Path difference

0 m

λ

Wavelength

0.78 m

1. Use the path-to-phase relation

Use

Δ ϕ = \frac{2 π Δ r}{λ}

2. Substitute the live path difference

Δ ϕ = \frac{2 π ( 0 )}{0} .78

3. Convert the extra distance into phase

That path difference is about 0 wavelengths of extra travel, so the wrapped phase comparison is 0 rad.

Current phase split

Δ ϕ = 0 rad

The path difference is close to a whole wavelength count, so the two slit contributions reinforce and the probe sits on a bright fringe.

Quick test

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Accessibility

Open the text-first descriptions when you need the simulation and graph translated into words.

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 is used to inspect the local probe field.

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Starter track

Step 3 of 5

Wave Optics

Double-Slit Interference appears later in this track, so it is cleaner to start from the beginning first.

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