Distinguish grazing refraction from total internal reflection
Refraction changes direction when a wave crosses a stationary boundary between different propagation speeds. For light, index n is the vacuum speed divided by the medium phase speed. Snell law is n1 sinθ1=n2 sinθ2, with both angles measured from the normal. The boundary preserves frequency; changing speed therefore changes wavelength rather than requiring the source to change its oscillation rate.
Learning outcome: Compare a=.75,1,1.25 for each allowed second index. Record the branch before calculating a transmitted angle. Explain why a field-amplitude or power claim cannot be inferred solely from a geometric direction drawing.
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.
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For n1=1.5,n2=1, the critical sine is 2/3 and critical angle is about 41.8103°. At a=.75, the transmitted angle is arcsin(.75)≈48.5904° while incidence is arcsin(.5)=30°. At a=1 the transmitted angle is exactly 90°; at a=1.25 no propagating transmitted angle is listed.
Open the experimentPredict
Exactly at the critical angle, the geometric transmitted direction is:
Experiment
Compare a=.75,1,1.25 for each allowed second index. Record the branch before calculating a transmitted angle. Explain why a field-amplitude or power claim cannot be inferred solely from a geometric direction drawing.
Keep grazing transmission separate from total reflection
Worked teaching model · synthetic values · Light crosses from index1.5 toward the second medium. sin(theta_i)=a*n2/1.5, so a is the candidate transmitted sine. Exactly a=1 gives grazing refraction; a>1 has no propagating transmitted ray in geometric optics. No Fresnel power or evanescent-field amplitude calculation.
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Geometric directions at the index boundary
Spatial axes use the same pixels per physical unit, preserving geometry. 1: incident ray toward interface (solid).2: reflected ray (dashed).3: interface (dotted).4: grazing transmitted geometric direction (dotted). Joined curves show the supplied model, not additional observations.
Equivalent numerical coordinates for Geometric directions at the index boundary
incident ray toward interface
| x (common length unit) | y (common length unit) |
|---|---|
| -0.666667 | 0.745356 |
| 0 | 0 |
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.
reflected ray
| x (common length unit) | y (common length unit) |
|---|---|
| 0 | 0 |
| 0.666667 | 0.745356 |
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.
interface
| x (common length unit) | y (common length unit) |
|---|---|
| -1 | 0 |
| 1 | 0 |
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.
grazing transmitted geometric direction
| x (common length unit) | y (common length unit) |
|---|---|
| 0 | 0 |
| 1 | 0 |
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 |
|---|---|---|
| Incident angle from normal | 41.8103 | degrees |
| Critical incident angle | 41.8103 | degrees |
| Candidate transmitted sine | 1 | ratio |
| Propagating transmitted ray exists | 1 | flag |
| Grazing boundary | 1 | flag |
| Total internal reflection branch | 0 | flag |
| Transmitted angle from normal | 90 | degrees |
Exactly at the critical angle the refracted direction is tangent, not a downward-propagating bulk ray.
n1 sin(theta_i)=n2 sin(theta_t), with all angles from the normal. The chosen control a is sin(theta_t) if a propagating geometric ray exists. At a=1 the refracted angle is90 degrees; above it no real angle is reported. This plot does not assign Fresnel power fractions or an evanescent-field amplitude. For a parallel slab with equal exterior media the final direction returns to the initial direction but a lateral displacement can remain.
Predict before inspecting the values. Save contrasting records with assumptions and one alternative explanation. This virtual display does not certify practical measurement technique.
Exactly at the critical angle the refracted direction is tangent, not a downward-propagating bulk ray.
n1 sin(theta_i)=n2 sin(theta_t), with all angles from the normal. The chosen control a is sin(theta_t) if a propagating geometric ray exists. At a=1 the refracted angle is90 degrees; above it no real angle is reported. This plot does not assign Fresnel power fractions or an evanescent-field amplitude. For a parallel slab with equal exterior media the final direction returns to the initial direction but a lateral displacement can remain.
Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.
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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?
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