Total Internal Reflection: The Critical Angle
1 · Predict
Light traveling from a denser medium (like glass) toward a less dense one (like air) can reflect entirely instead of refracting out, if the incidence angle is steep enough. Does a higher-index glass have a smaller or larger critical angle?
- A higher-index glass has a smaller critical angle — total internal reflection kicks in more easily.
- A higher-index glass has a larger critical angle.
- The critical angle doesn't depend on the glass's index.
2 · Set Up
- Open the tir preset and press Reset. Light travels from glass into air (n₂ = 1.0 fixed).
- Enable the critical-angle readout.
- Set the glass's refractive index for each trial and record the critical angle.
3 · Collect Data
| Glass index n₁ | Critical angle θ_c (°) |
|---|---|
| 1.3 | |
| 1.5 | |
| 1.7 |
Plot critical angle θ_c (y-axis) against 1/n₁ (x-axis) for your three trials.
4 · Analyze
- For one trial, compute θ_c = asin(n₂/n₁) using n₂ = 1.0. Compare to the table.
- Explain why a higher-index glass (bending light more strongly) has a SMALLER critical angle — total internal reflection happens for a wider range of incidence angles.
5 · Extend
- Optical fibers rely on total internal reflection to trap light inside a high-index glass core, bouncing it along the fiber's length with almost no loss. Explain why fiber-optic cable manufacturers use very high-index glass cores surrounded by lower-index cladding.
- Diamond has an unusually high refractive index (about 2.42), giving it a very small critical angle (about 24°). Explain why this makes a well-cut diamond sparkle brilliantly — light entering from the top tends to totally internally reflect multiple times before exiting.
The Physics Behind This Experiment
Critical Angle for Total Internal Reflection
Light traveling from a denser medium (n₁) toward a less dense one (n₂ < n₁) totally internally reflects for any incidence angle beyond the critical angle θ_c = asin(n₂/n₁). Beyond this angle, no light transmits at all — 100% reflection.