A Demonstration of the Critical Angle Without Using Total Internal Reflection
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
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.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it