OpticsIntermediateStarter track

Concept module

Diffraction

Watch a wave spread after one narrow opening, see why diffraction grows when wavelength competes with slit width, and build the wave-optics bridge toward double-slit interference.

Interactive lab

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

Time

0.00 s / 2.50 sLivePause to inspect a specific moment, then step or scrub through it.

0.00 s2.50 s

Diffraction

One slit feeds one screen, so opening width, wavelength, and spatial spread stay tied to the same live geometry.

Live setup

Graphs

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

Probe field

Tracks the slit-center oscillation, the current probe field, and the local diffraction envelope at that screen point.

time (s): 0 to 2.5field / displacement (a.u.): -1.05 to 1.05

Slit centerProbe field+ 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

l amb d a

1 m

Longer wavelength makes the same opening spread the wave more strongly.

Slit width

a

2.4 m

A narrower opening broadens the central diffraction peak.

Probe height

y_{p}

0.6 m

Moves the screen probe to a new point on the diffraction 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 of the pattern is not just bright. It is also the widest part of the single-slit envelope, and that width changes when lambda / a changes.

Try this

Start from Center bright, then compare Wide slit with Broad spread before reading the graph.

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.

l amb d a

Wavelength

1 m

Longer wavelength increases the amount of spreading for the same opening width.

Graph: Screen patternGraph: Probe fieldOverlay: Slit-width guideOverlay: First-minimum guideOverlay: Edge paths

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 prompt at a time so the spread pattern stays tied to the same slit geometry, screen strip, and graph.

ObservationPrompt 1 of 1

Notice that the center of the pattern is not just bright. It is also the widest part of the single-slit envelope, and that width changes when lambda / a changes.

Try this

Start from Center bright, then compare Wide slit with Broad spread before reading the graph.

Why it matters

The main teaching target is spread, not only brightness.

Control: WavelengthControl: Slit widthGraph: Screen patternOverlay: Slit-width 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

Slit-width guide

Marks the opening width directly on the barrier.

What to notice

The opening itself is part of the physics. Changing a changes how much of the wave launches the outgoing pattern.

Why it matters

It keeps the aperture size visible instead of treating diffraction as a disconnected graph effect.

Control: Slit widthGraph: Screen patternEquation

a

Challenge mode

Turn the spread pattern into small wave-optics hunts that stay tied to the same slit geometry.

0/2 solved

ConditionCore

1 of 4 checks

Find the first dark band

Starting from Center bright, move the probe onto the first dark band without changing the slit or wavelength.

Graph-linkedGuided start2 hints

Suggested start

Drag the probe instead of changing the opening.

Pending

Open the Screen pattern graph.

Probe field

Matched

Keep the Edge paths visible.

Pending

Bring the edge-path split close to one wavelength.

0.26

Pending

Drive the relative intensity below 0.08.

0.8

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 = 0.6 m with edge-to-edge path difference 0.26 m. The current lambda/a ratio is 0.42, so the probe field has envelope 0.89 and relative intensity 0.8. The first minimum sits near 25.06°.

Equation detailsDeeper interpretation, notes, and worked variable context.

Edge-to-edge path difference

The top and bottom of the slit feed the same screen point with slightly different path lengths.

Δ r_{e d g e} \approx a sin θ

The live stage keeps the exact edge paths visible while the equation gives the far-screen approximation.

a

Slit width 2.4 m

y_{p}

Probe height 0.6 m

Envelope angle

Packages the opening-width and wavelength comparison into one quantity for the diffraction envelope.

β = \frac{π a sin θ}{λ} \approx \frac{π Δ r _{e d g e}}{λ}

l amb d a

Wavelength 1 m

a

Slit width 2.4 m

y_{p}

Probe height 0.6 m

Single-slit intensity

The bright central region and weaker side regions come from the square of the diffraction envelope.

\frac{I}{I _{0}} = (\frac{sin β}{β})^{2}

l amb d a

Wavelength 1 m

y_{p}

Probe height 0.6 m

First minimum

The first dark point appears when the edge-to-edge path difference grows to one wavelength.

sin θ_{1} \approx \frac{λ}{a}

l amb d a

Wavelength 1 m

a

Slit width 2.4 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 2 of 50 / 5 complete

Wave Optics

Earlier steps still set up Diffraction.

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

Previous step: Polarization.

Start from track beginning

Short explanation

What the system is doing

Diffraction is the spreading of a wave after it passes through a narrow opening or around an edge. A wide opening lets the outgoing wave stay relatively straight, but once the opening width and wavelength become comparable the wave no longer stays tightly collimated.

This page keeps the geometry intentionally bounded: one slit, one screen, and one movable probe. The same slit width, wavelength, and probe height drive the stage, the pattern graph, prediction mode, worked examples, and challenge checks so the pattern stays tied to one honest wave-optics story instead of a giant optics lab.

Key ideas

01Diffraction becomes more noticeable when the wavelength is large relative to the slit width, so the central peak spreads out instead of staying narrow.

02The screen pattern is not random blur. It follows a single-slit envelope with clear bright and dim regions set by the edge-to-edge path difference across the opening.

03A double-slit pattern still depends on diffraction because each slit has its own spreading envelope before the two slits interfere with one another.

Live diffraction checks

Solve the exact state on screen.

These examples read the current slit geometry directly from the live state, so the algebra stays attached to the same pattern you are seeing on the screen.

Live valuesFollowing current parameters

For the current slit width a = 2.4 and wavelength lambda = 1, where should the first diffraction minimum appear?

a

Slit width

2.4 m

l amb d a

Wavelength

1 m

l amb d a / a

Wavelength-to-slit ratio

0.42

1. Start from the first-minimum condition

Use the single-slit condition

sin (θ_{1}) \approx λ / a

2. Substitute the live opening and wavelength

sin (θ_{1}) \approx 1/2.4 = 0.42

3. Read the geometric consequence

θ_{1} = sin^{- 1} (0.42) = 25.0 6^{\circ}

First-minimum result

θ_{1} = 25.0 6^{\circ}

The first minimum sits about 25.06^\circ from the center, so the central peak spans roughly 5.05 m on the screen.

Spread-width checkpoint

You want the central diffraction peak to spread out without moving the screen. Which control change is the most reliable move?

Prediction prompt

Choose whether you should change the wavelength, the slit width, or the probe position.

Check your reasoning

Increase the wavelength or decrease the slit width so the ratio lambda / a gets larger.

Probe position only samples a different part of the existing pattern. The actual spread changes when the wavelength becomes larger relative to the opening.

Common misconception

A narrower opening always makes the outgoing beam narrower because less of the wave gets through.

A narrower opening reduces the width of the source region, but it also increases the spreading of the outgoing wave.

That is why the central diffraction peak broadens when the opening gets smaller relative to the wavelength.

Quick test

Variable effect

Question 1 of 4

Answer from the live spread logic, not from isolated buzzwords.

Which change makes diffraction more noticeable for the same screen distance?

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 plane wavefronts reaching a barrier with one vertical slit. On the right side, curved outgoing wavefronts spread from the opening toward a screen strip that brightens or dims according to the diffraction intensity.

A movable probe marks one screen point. Optional overlays show the slit width, the top and bottom edge paths to the probe, and the first-minimum guide when the current ratio lambda / a gives a finite first minimum.

Graph summary

The probe-field graph shows the oscillation at the slit center and the current probe point, with dashed envelope lines marking the local diffraction amplitude.

The screen-pattern graph shows relative intensity against screen height, so it remains a spatial map while the time rail inspects the local probe field.

Carry wave optics forward

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.

Two-slit patternOptics

Diffraction

See each variable before you move it.

Slit-width guide

Find the first dark band

Wave Optics

What the system is doing

Solve the exact state on screen.

For the current slit width a = 2.4 and wavelength lambda = 1, where should the first diffraction minimum appear?

Which change makes diffraction more noticeable for the same screen distance?

Keep moving through the concept map.

Double-Slit Interference

Optical Resolution / Imaging Limits

Wave Interference