Separate an angular baseline from wavelength dependence
A measured deviation angle may contain both refraction and an instrument zero error. For a thin prism at small angles, the supplied first-order relation is δ≈(n−1)A, where A is prism apex angle and n the refractive index relative to the surrounding air approximation. A common angular readout offset adds a constant. All angles must use a consistent unit in this first-order relation.
Learning outcome: Fit red index and angular offset from two records, freeze the third-angle prediction and then reveal it. Compare the separately supplied blue prediction and state which additional wavelength observation would actually test dispersion. Explain why a red-only fit is insufficient for that claim.
Starting recap
Use normal-based angles, signed conjugate distances and explicit optical-path/reflection phases. Separate geometric direction, amplitude and energy; preserve focal and critical boundaries.
All lessons are open directly. Your saved experiments remain when you leave and return.
Try
At reference angle4° and offset+.1°, red indications at4° and8° are2.1° and4.1°. Their difference recovers nred−1=.5 and offset+.1°. The unused12° prediction is6.1° within the first-order model. The independently supplied blue index predicts2.26° at4°, a blue-minus-red difference.16°.
Open the experimentPredict
What can two red readings at known distinct prism angles identify in this model?
Experiment
Fit red index and angular offset from two records, freeze the third-angle prediction and then reveal it. Compare the separately supplied blue prediction and state which additional wavelength observation would actually test dispersion. Explain why a red-only fit is insufficient for that claim.
Separate angle baseline from dispersion evidence
Worked teaching model · synthetic values · Supplied thin-prism first-order law delta=(n−1)A for small angles, plus common angular offset. Red index1.50 and separately supplied blue index1.54. Red records at A and2A calibrate nred and offset; red3A is fresh validation of this approximate law. Blue index is not inferred from red-only data.
Reset keeps your prediction, captures and practice history.
Thin-prism calibration and unused red comparison
Unlike graph quantities rescale independently; read units and values, not screen angles. 1: red fit from first two angles (solid).2: fresh red third-angle record (filled markers).3: blue using separately supplied dispersion (filled markers). Joined curves show the supplied model, not additional observations.
Equivalent numerical coordinates for Thin-prism calibration and unused red comparison
red fit from first two angles
| prism angle (degrees) | indicated deviation (degrees) |
|---|---|
| 0 | 0.1 |
| 0.15 | 0.175 |
| 0.3 | 0.25 |
| 0.45 | 0.325 |
| 0.6 | 0.4 |
| 0.75 | 0.475 |
| 0.9 | 0.55 |
| 1.05 | 0.625 |
| 1.2 | 0.7 |
| 1.35 | 0.775 |
| 1.5 | 0.85 |
| 1.65 | 0.925 |
| 1.8 | 1 |
| 1.95 | 1.075 |
| 2.1 | 1.15 |
| 2.25 | 1.225 |
| 2.4 | 1.3 |
| 2.55 | 1.375 |
| 2.7 | 1.45 |
| 2.85 | 1.525 |
| 3 | 1.6 |
| 3.15 | 1.675 |
| 3.3 | 1.75 |
| 3.45 | 1.825 |
| 3.6 | 1.9 |
| 3.75 | 1.975 |
| 3.9 | 2.05 |
| 4.05 | 2.125 |
| 4.2 | 2.2 |
| 4.35 | 2.275 |
| 4.5 | 2.35 |
| 4.65 | 2.425 |
| 4.8 | 2.5 |
| 4.95 | 2.575 |
| 5.1 | 2.65 |
| 5.25 | 2.725 |
| 5.4 | 2.8 |
| 5.55 | 2.875 |
| 5.7 | 2.95 |
| 5.85 | 3.025 |
| 6 | 3.1 |
| 6.15 | 3.175 |
| 6.3 | 3.25 |
| 6.45 | 3.325 |
| 6.6 | 3.4 |
| 6.75 | 3.475 |
| 6.9 | 3.55 |
| 7.05 | 3.625 |
| 7.2 | 3.7 |
| 7.35 | 3.775 |
| 7.5 | 3.85 |
| 7.65 | 3.925 |
| 7.8 | 4 |
| 7.95 | 4.075 |
| 8.1 | 4.15 |
| 8.25 | 4.225 |
| 8.4 | 4.3 |
| 8.55 | 4.375 |
| 8.7 | 4.45 |
| 8.85 | 4.525 |
| 9 | 4.6 |
| 9.15 | 4.675 |
| 9.3 | 4.75 |
| 9.45 | 4.825 |
| 9.6 | 4.9 |
| 9.75 | 4.975 |
| 9.9 | 5.05 |
| 10.05 | 5.125 |
| 10.2 | 5.2 |
| 10.35 | 5.275 |
| 10.5 | 5.35 |
| 10.65 | 5.425 |
| 10.8 | 5.5 |
| 10.95 | 5.575 |
| 11.1 | 5.65 |
| 11.25 | 5.725 |
| 11.4 | 5.8 |
| 11.55 | 5.875 |
| 11.7 | 5.95 |
| 11.85 | 6.025 |
| 12 | 6.1 |
At most 82 representative computed coordinates including endpoints; the plotted curve can use a finer grid. A table of a revealed generator is not independent measurement evidence.
fresh red third-angle record
| prism angle (degrees) | indicated deviation (degrees) |
|---|---|
| 12 | 6.1 |
At most 82 representative computed coordinates including endpoints; the plotted curve can use a finer grid. A table of a revealed generator is not independent measurement evidence.
blue using separately supplied dispersion
| prism angle (degrees) | indicated deviation (degrees) |
|---|---|
| 4 | 2.26 |
At most 82 representative computed coordinates including endpoints; the plotted curve can use a finer grid. A table of a revealed generator is not independent measurement evidence.
| Quantity | Value | Unit |
|---|---|---|
| First red angle indication | 2.1 | degrees |
| Second red angle indication | 4.1 | degrees |
| Inferred red refractive index | 1.5 | ratio |
| Recovered angular offset | 0.1 | degrees |
| Fresh red third-angle indication | 6.1 | degrees |
| Predicted red third-angle indication | 6.1 | degrees |
| Blue indication from independently supplied index | 2.26 | degrees |
| Blue-minus-red indication at first prism angle | 0.16 | degrees |
A common angular offset cancels in differences; dispersion still needs wavelength-dependent evidence.
The first-order thin-prism relation is delta=(n−1)A. Two red records at A and2A identify slope nred−1 and additive baseline within that approximate model;3A is an unused prediction. A blue index supplied independently gives stronger deviation here. Red-only data cannot infer the blue index or a full dispersion curve. At a stationary interface frequency stays fixed while wavelength becomes lambda0/n; the changed direction is not a changed source frequency.
Predict before inspecting the values. Save contrasting records with assumptions and one alternative explanation. This virtual display does not certify practical measurement technique.
A common angular offset cancels in differences; dispersion still needs wavelength-dependent evidence.
The first-order thin-prism relation is delta=(n−1)A. Two red records at A and2A identify slope nred−1 and additive baseline within that approximate model;3A is an unused prediction. A blue index supplied independently gives stronger deviation here. Red-only data cannot infer the blue index or a full dispersion curve. At a stationary interface frequency stays fixed while wavelength becomes lambda0/n; the changed direction is not a changed source frequency.
Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.
Understand
Apply
Public practice checks a specific claim. It does not establish independent mastery.
Which independent observation would reject the approximation, sign convention or calibration premise rather than merely refit it?
Continue
Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.
Skipping retains experiments and awards no mastery.
Save a science backup or import one
Science work is stored locally in this browser, separately from mathematics and AI. It does not sync automatically. Use this science-only backup; this checkout's older all-subject export does not include science.
A legacy file is available only when the complete snapshot fits the 36 MB limit. For larger snapshots, prepare a complete file set below; never discard notebooks to make a smaller file.
Matching imported notebook drafts replace their current drafts. Omitted lessons and known first attempts remain. Export your current work first if you want to retain both drafts.
Complete file sets and course backups
A file set can hold more work than one science file. Keep its manifest and every part together. Each file is limited to 36 MB. This format needs this version of LearnAI or a compatible newer version; older versions can use only the legacy single-file backup above.
The set includes every saved science course and global continuation at this moment. Later edits need a new export. A conflicting tab exports its own visible work, which may differ from saved work in another tab.
0 file(s) selected. File order and filenames do not determine identity. Missing, changed or conflicting parts block the entire restore; no good part is applied by itself.
Science storage: loading. No account or remote computation is required.