A Demonstration of the Critical Angle Without Using Total Internal Reflection
Bibliographic record
Abstract
The success of a light ray's transmission to a medium of lower index of refraction depends upon its incident angle at the boundary. If this angle, when measured from the normal, is greater than a certain critical angle, the ray will reflect totally, remaining in the high-index medium. Snell's law, which says that n1 sin θ1 = n2 sin θ2, easily gives the critical angle as θ1 = sin−1(n2/n1) by setting the angle of refraction to θ2 = 90°. Demonstrations of the critical angle phenomenon usually work with this operational definition. For example, as in Fig. 1, one directs a beam of light radially through the curved surface of a semicircular piece of glass and rotates the semicircle until no ray is seen exiting the flat surface. We describe here a demonstration of the critical angle that does not employ rays leaving the higher-index medium but entering it.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".