OpticsIntermediateStarter track

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.

Interactive lab

Keep the stage, graph, and immediate control feedback in one working view.

Time

0.00 s / 2.40 sLivePause to inspect a specific moment, then step or scrub through it.

0.00 s2.40 s

Double-Slit Interference

Two narrow slits feed one screen, so path difference, phase, and fringe spacing stay tied to the same optics bench.

Live setup

Graphs

Switch graph views without breaking the live stage and time link.

Probe field

Tracks the two slit contributions and the live resultant at the selected probe point.

time (s): 0 to 2.4field / displacement (a.u.): -2.1 to 2.1

Slit 1Slit 2Resultant+ envelope- envelope

Hover or scrub to link the graph back to the stage.time (s) / field / displacement (a.u.)

Controls

Adjust the physical parameters and watch the motion respond.

Wavelength

λ

0.78 m

Longer wavelength widens the fringe spacing for the same slit geometry.

Slit separation

d

2.6 m

Increasing slit separation tightens the fringes by increasing the path-difference gradient.

Screen distance

L

5.4 m

Moving the screen farther turns the same interference angles into larger fringe spacing.

Probe height

y_{p}

0.8 m

Moves the sampled screen point without changing the underlying fringe pattern.

More tools

Secondary controls, alternate presets, and less-used toggles stay nearby without crowding the main bench.

Show

More presets

Presets

Predict -> manipulate -> observe

Keep the active prompt next to the controls so each change has an immediate visible consequence.

ObservationPrompt 1 of 1

Notice that the center line is bright because the two paths are equal there, so the phase split is close to zero.

Try this

Start from Center bright, then move the probe upward until the strip first turns dark.

Equation map

See each variable before you move it.

Select a symbol to highlight the matching control and the graph or overlay it most directly changes.

λ

Wavelength

0.78 m

Longer wavelength makes the same path difference count for less phase per meter and spreads the fringes farther apart.

Graph: Screen patternGraph: Probe fieldOverlay: Path-difference guideOverlay: Fringe-spacing guideOverlay: Phase wheel

Equations in play

Choose an equation to sync the active symbol, control highlight, and related graph mapping.

More tools

Detailed noticing prompts, guided overlays, and challenge tasks stay available without taking over the main bench.

Hide

What to notice

Use one cue at a time so the same slit geometry, probe, and pattern graph stay easy to compare.

ObservationPrompt 1 of 1

Notice that the center line is bright because the two paths are equal there, so the phase split is close to zero.

Try this

Start from Center bright, then move the probe upward until the strip first turns dark.

Why it matters

It anchors the pattern on a simple reference point before you read the off-center fringes.

Control: Probe heightGraph: Screen patternOverlay: Path-difference guide

Guided overlays

Focus one overlay at a time to see what it represents and what to notice in the live motion.

2 visible

Overlay focus

Geometry guide

Marks slit separation and screen distance directly on the stage.

What to notice

The same d and L values that label the stage also control the fringe spacing equation.

Why it matters

It keeps the optics geometry visible instead of treating the pattern as a disconnected graph effect.

Control: Slit separationControl: Screen distanceGraph: Screen patternEquation

d

Equation

L

Challenge mode

Turn the fringe pattern into compact optics hunts that stay tied to the same slit geometry and live probe.

0/2 solved

ConditionCore

3 of 4 checks

Find the first dark fringe

Starting from Center bright, move the probe onto the first dark fringe without changing wavelength, slit separation, or screen distance.

Graph-linkedGuided start2 hints

Suggested start

Use the pattern graph as the guide while you move only the probe.

Pending

Open the Screen pattern graph.

Probe field

Matched

Keep the Path-difference guide visible.

Matched

Bring the path difference close to half a wavelength.

0.48

Matched

Drive the relative intensity below 0.08.

5.93e-3

The checklist updates from the live simulation state, active graph, overlays, inspect time, and compare setup.

At t = 0 s, the probe is at y = 0.8 m on a screen 5.4 m away from slits separated by 2.6 m. The path difference is 0.37 m, giving a phase split of 2.99 rad and dark interference at that point. The approximate bright-fringe spacing is 1.62 m.

Equation detailsDeeper interpretation, notes, and worked variable context.

Path difference

One slit-to-screen path can be slightly longer than the other for the same screen point.

Δ r = r_{2} - r_{1}

The stage keeps both path lengths visible while the probe moves.

y_{p}

Probe height 0.8 m

Phase difference

Path difference matters only through how many wavelengths of extra travel it represents.

Δ ϕ = \frac{2 π Δ r}{λ}

λ

Wavelength 0.78 m

y_{p}

Probe height 0.8 m

Bright fringes

Constructive interference occurs when the path difference matches a whole-number multiple of the wavelength.

d sin θ = mλ

λ

Wavelength 0.78 m

d

Slit separation 2.6 m

Dark fringes

Destructive interference occurs when the path difference is a half-number multiple of the wavelength.

d sin θ = (m + \frac{1}{2}) λ

λ

Wavelength 0.78 m

d

Slit separation 2.6 m

y_{p}

Probe height 0.8 m

Fringe spacing

For small angles, wavelength and geometry together set how far apart neighboring bright fringes appear on the screen.

Δ y \approx \frac{λ L}{d}

λ

Wavelength 0.78 m

d

Slit separation 2.6 m

L

Screen distance 5.4 m

Progress

Not startedMastery: NewLocal-first

Start exploring and Open Model Lab will keep this concept's progress on this browser first. Challenge mode has 2 compact tasks ready. No finished quick test, solved challenge, or completion mark is saved yet.

Let the live model runChange one real controlOpen What to notice

Try this setup

Copy the live bench state and reopen this concept with the same controls, graph, overlays, and compare context.

Stable links

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

Short explanation

What the system is doing

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.

Live double-slit checks

Solve the exact state on screen.

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.

Live valuesFollowing current parameters

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

y_{p}

Probe height

0.8 m

Δ r

Path difference

0.37 m

λ

Wavelength

0.78 m

1. Start from the interference relation

Use

Δ ϕ = \frac{2 π Δ r}{λ}

2. Substitute the live geometry

Δ ϕ = \frac{2 π ( 0.37 )}{0} .78

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

Δ ϕ = 2.99 rad

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?

Prediction prompt

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

Check your reasoning

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?

Choose one answer to reveal feedback, then test the idea in the live system if a guided example is available.

Accessible description

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.

Carry interference deeper into optics

Keep moving through the concept map.

These suggestions come from the concept registry, so the reason label reflects either curated guidance or the fallback progression logic.

Boundary opticsOptics

Double-Slit Interference

See each variable before you move it.

Geometry guide

Find the first dark fringe

Wave Optics

What the system is doing

Solve the exact state on screen.

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

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

Keep moving through the concept map.

Refraction / Snell's Law

Total Internal Reflection

Photoelectric Effect