Optics
Total internal reflection
Beyond the critical angle no light escapes — the ray is totally reflected back into the denser medium (θc = arcsin(n₂/n₁)).
Total internal reflection — interactive Optics simulation. Beyond the critical angle no light escapes — the ray is totally reflected back into the denser medium (θc = arcsin(n₂/n₁)).
Total internal reflection
Beyond the critical angle no light escapes — the ray is totally reflected back into the denser medium (θc = arcsin(n₂/n₁)).
When light travels from a denser to a rarer medium, increasing the incident angle eventually reaches the critical angle where refracted rays would graze the surface. Beyond θ_c all energy reflects internally—principle behind fiber optics and diamond brilliance.
- θ_c = arcsin(n₂/n₁)
- No transmission past θ_c
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
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?
Predictions to weigh
- A higher-index glass has a larger critical angle.
- The critical angle doesn't depend on the glass's index.
- A higher-index glass has a smaller critical angle — total internal reflection kicks in more easily.
Variable roles
What you set:
- Glass index n₁
What you measure:
- Critical angle θ_c (°)
How the investigation runs
- 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.
Governing equation
Critical Angle for Total Internal Reflection — θc = arcsin(n₂/n₁)
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.
What the printable worksheet asks students to work out
- 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.
Where this shows up beyond the lab
- 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.
- AP Physics 2 — Unit 13: Geometric Optics
- General High School Physics — Light & optics
- NGSS High School Physics — Wave properties
- Welcome to Tir
- Select the object
- Press Play
- No light transmitted
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.