OpticsIntermediateStarter track

Concept module

Dispersion / Refractive Index and Color

Use one compact thin-prism bench to see how refractive index can depend on wavelength, why different colors bend by different amounts, and how a bounded prism model separates colors without widening into a full spectroscopy subsystem.

Interactive lab

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

One thin prism, one color-dependent refractive-index model, and one response-graph pair stay tied together so color separation stays a refraction story instead of a separate subsystem. The outgoing fan uses a small display magnification so the color order stays readable while the card keeps the real angles.

Live prism

Graphs

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

Refractive index vs wavelength

Shows how the same material model assigns a slightly different refractive index to each visible wavelength.

vacuum wavelength lambda_0 (nm): 420 to 680n(lambda): 1.19 to 1.54

n(lambda)

Hover or scrub to link the graph back to the stage.vacuum wavelength lambda_0 (nm) / n(lambda)

Controls

Adjust the physical parameters and watch the motion respond.

Selected wavelength

λ

550 nm

Moves the selected visible color from violet toward red.

Reference index near green

n_{ref}

1.52

Raises or lowers the overall refractive-index baseline.

Dispersion strength

D

0.02

Sets how strongly short and long wavelengths separate in refractive index.

Prism angle

A

18°

Widens or narrows the thin prism.

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.

Graph readingPrompt 1 of 2

Notice that these graphs compare different wavelengths for one prism state. Hovering them previews another wavelength immediately instead of advancing time.

Try this

Hover near the red end of the deviation graph, then near the violet end, and watch the selected ray jump between those wavelengths on the same prism.

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

Selected wavelength

550 nm

Moves the selected color from red toward violet so you can read how n(lambda) and prism deviation change together.

Graph: Refractive index vs wavelengthGraph: Thin-prism deviation vs wavelengthOverlay: Color fanOverlay: Index guide

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

Stay with one wavelength-dependent bend story at a time. The prism fan, the readout card, and the graphs all come from the same bounded model.

Graph readingPrompt 1 of 2

Graph: Refractive index vs wavelength

Notice that these graphs compare different wavelengths for one prism state. Hovering them previews another wavelength immediately instead of advancing time.

Try this

Hover near the red end of the deviation graph, then near the violet end, and watch the selected ray jump between those wavelengths on the same prism.

Why it matters

It keeps the graph honest: this is a wavelength family, not a time trace.

Graph: Refractive index vs wavelengthGraph: Thin-prism deviation vs wavelength

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

Color fan

Shows red, green, and violet outgoing rays together with the current spread bracket.

What to notice

Violet sits below red because it uses the larger refractive index in this visible range.

Why it matters

It turns dispersion into a geometric refraction story rather than a vocabulary list about prisms.

Control: Selected wavelengthControl: Dispersion strengthControl: Prism angleGraph: Thin-prism deviation vs wavelengthEquation

λ

Equation

D

Equation

A

Challenge mode

Use the live prism, not a detached puzzle state. The checks read the current wavelength, prism angle, and wavelength-dependent index from the same bounded model you are editing.

0/2 solved

MatchStretch

0 of 8 checks

Compare a weak and strong disperser

Open compare mode from Crown green. Keep Setup A weakly dispersive, then edit Setup B until the same prism angle produces a much larger red-violet spread.

Compare modeGraph-linkedGuided start2 hints

Suggested start

Leave Setup A as the weakly dispersive baseline while you edit Setup B.

Pending

Open the deviation graph.

Refractive index vs wavelength

Pending

Edit Setup B while compare mode is active.

Explore

Pending

Keep Setup A weakly dispersive.

Pending

Keep both prism angles in the same moderate range.

Pending

Make Setup B strongly dispersive.

Pending

Keep Setup B near the same prism-angle band.

Pending

Keep Setup A with only a small red-violet spread.

Pending

Make Setup B show a much larger red-violet spread.

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

For 550 nm, the bounded thin-prism model gives n(lambda) = 1.52 and a prism deviation of about 9.36°. Shorter visible wavelengths bend more strongly here, so violet leaves about 0.28° below red across the same prism.

Equation detailsDeeper interpretation, notes, and worked variable context.

Bounded dispersion model

Keeps one wavelength-dependent refractive-index model in charge of the whole page.

n (λ) \approx n_{ref} + D [(\frac{λ _{ref}}{λ})^{2} - 1]

This page fixes \lambda_{\mathrm{ref}} = 550\,\mathrm{nm} so the reference index stays anchored near green light.

λ

Selected wavelength 550 nm

n_{ref}

Reference index 1.52

D

Dispersion strength 0.02

Speed from refractive index

A larger refractive index means a lower wave speed for that wavelength in the material.

v (λ) = \frac{c}{n ( λ )}

λ

Selected wavelength 550 nm

n_{ref}

Reference index 1.52

Thin-prism deviation

In the thin-prism limit, the total bend grows with both refractive index and prism angle.

δ (λ) \approx [n (λ) - 1] A

λ

Selected wavelength 550 nm

n_{ref}

Reference index 1.52

A

Prism angle 18°

Color spread

The red-violet separation grows when the material response becomes more wavelength dependent or when the prism angle gets larger.

Δ δ \approx [n (λ_{v}) - n (λ_{r})] A

D

Dispersion strength 0.02

A

Prism angle 18°

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 4 of 50 / 5 complete

Wave Optics

Earlier steps still set up Dispersion / Refractive Index and Color.

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

Previous step: Double-Slit Interference.

Start from track beginning

Short explanation

What the system is doing

This concept keeps dispersion tightly attached to the refraction story you already used on one boundary. The only new idea is that the refractive index does not have to stay the same for every wavelength, so different colors can obey slightly different bending rules in the same material.

One compact thin-prism bench now keeps wavelength, material response, prism angle, outgoing color fan, graph previews, worked examples, prediction mode, and challenge checks on the same bounded model. The goal is to explain prism color separation honestly without widening into a full spectroscopy platform.

Key ideas

01Dispersion means the refractive index depends on wavelength, so shorter visible wavelengths can use a slightly larger n than longer ones in the same material.

02If violet uses the larger refractive index, it bends more strongly than red at the same prism.

03A prism does not create colors from nothing. It separates wavelengths that were already present by bending them by different amounts.

04This page uses a bounded thin-prism model: the graph values and readout card keep the real deviation angles, while the stage lightly magnifies the outgoing fan so the color order stays readable.

Live dispersion checks

Solve the exact state on screen.

Read the current prism state directly from the live controls. The same wavelength-dependent index model drives the stage, the outgoing fan, and the response graphs.

Live valuesFollowing current parameters

For the current wavelength and material, what refractive index does the selected color use?

λ

Selected wavelength

550 nm

n_{ref}

Reference index

1.52

D

Dispersion strength

0.02

1. Start from the bounded dispersion model

Use

n (λ) \approx n_{ref} + D [(\frac{550}{λ})^{2} - 1]

with wavelengths in nanometers.

2. Evaluate the wavelength term

For

λ = 550 nm

, the bracket becomes

(\frac{550}{550})^{2} - 1 = 0

3. Build the current index

n (λ) \approx 1.52 + 0.02 (0) = 1.52

Current refractive index

n (λ) \approx 1.52

At 550 nm, the current green ray uses n(lambda) = 1.52, so the thin-prism bend is larger than red but smaller than violet in the same material.

Prism-spread checkpoint

You keep the same prism angle and the same green reference index, but you raise the dispersion strength. Before touching the controls, which color should peel away the most from the others?

Prediction prompt

Answer from the wavelength-dependent index, not from a brightness cue.

Check your reasoning

Violet should separate the most because it uses the largest refractive index in this visible range.

Raising the dispersion strength makes the difference between short- and long-wavelength refractive indices larger. That gives violet the largest bend and widens the outgoing fan most strongly on the short-wavelength side.

Common misconception

A prism paints color onto white light because the glass somehow adds red on one side and violet on the other.

The prism is not adding new visible colors. It is separating wavelengths that were already present in the beam because each wavelength can use a different refractive index in the material.

That is why a no-dispersion model can still bend the beam overall while failing to spread red and violet apart.

Quick test

Variable effect

Question 1 of 4

Answer from the live wavelength-dependent refraction story, not from a vague picture of a rainbow beam.

In a dispersive prism, which visible color bends more at the same prism angle?

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 one triangular thin-prism sketch with a white incoming beam, a highlighted selected-color ray, and optional red, green, and violet comparison rays leaving the same prism. A readout card summarizes the current wavelength, reference index, dispersion strength, selected refractive index, selected deviation, speed fraction, red-violet spread, and prism angle.

Optional overlays can show the outgoing color fan, the current ordering of red, green, and violet refractive indices, and the bounded thin-prism approximation used to connect refractive index to total deviation. The stage uses a small display magnification so the color order stays readable while the card and graphs keep the real angle values.

Graph summary

The first graph plots refractive index against visible wavelength for the current material model. The second plots thin-prism deviation against visible wavelength for the same material and prism angle, so hovering either graph previews another wavelength on the same static prism instead of stepping time forward.

Carry color-dependent bending 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.

Critical-angle limitOptics

Dispersion / Refractive Index and Color

See each variable before you move it.

Color fan

Compare a weak and strong disperser

Wave Optics

What the system is doing

Solve the exact state on screen.

For the current wavelength and material, what refractive index does the selected color use?

In a dispersive prism, which visible color bends more at the same prism angle?

Keep moving through the concept map.

Total Internal Reflection

Lens Imaging

Atomic Spectra