Critical Angle & TIR

Overview

This lesson should feel like a direct extension of refraction and Snell’s law. Students need a clear sequence of ray diagrams so they can see what changes as the angle of incidence increases and why total internal reflection only happens under specific conditions.

Key knowledge and explanations

• Define the critical angle as the angle of incidence in the more optically dense medium for which the angle of refraction is 90°.
• Show a sequence of three diagrams for light travelling from glass to air: one angle below the critical angle, one exactly at the critical angle, and one above it. Keep the boundary, normal, and labelled angles consistent across all three.
• Make the two conditions for total internal reflection explicit: the ray must travel from a medium with higher refractive index to one with lower refractive index, and the angle of incidence must be greater than the critical angle.
• Model the critical-angle equation in a usable form, sin c = 1 / n, and link the answer back to the diagram rather than treating it as an isolated calculation.
• Use optical fibres as the main application, explaining that repeated total internal reflection keeps the signal inside the fibre over long distances.

Lesson flow

1. Start with two retrieval questions on refractive index and Snell’s law so students recall what happens when light moves from glass to air.
2. Demonstrate the changing refracted ray with a semicircular block or a clear sequence of diagrams, pausing when the refracted ray runs along the boundary to define the critical angle.
3. Model one calculation for critical angle from refractive index and one reverse calculation, with students annotating the diagram before they substitute values.
4. Finish with a short explanation task on why optical fibres work, using the language of higher refractive index, critical angle, and total internal reflection.

Checks for understanding

• Use a hinge question with three ray diagrams and ask which one shows the critical angle and which one shows total internal reflection.
• Give one quick calculation where students find c from n or find n from a given critical angle.
• Ask students to explain in one sentence why total internal reflection cannot happen when light travels from air into glass.

Common mistakes or misconceptions

• Students often think total internal reflection can happen whenever a ray hits a boundary. Keep returning to the two-condition checklist and test each example against it.
• Some confuse the critical angle with the angle of refraction. Reinforce that at the critical angle the refracted ray is along the boundary, so the refracted angle is 90°.
• Students may assume any reflected ray inside glass is total internal reflection. Contrast partial internal reflection below the critical angle with complete reflection above it.

Follow-up

• Set a short mix of diagram and equation questions so students practise switching between the qualitative and quantitative ideas.
• Carry forward the idea that refractive index affects ray behaviour, because the next lesson uses that idea to explain why different colours in white light separate in a prism.