Refractive Index & TIR: Defeating the Normal Line Trap

By Sarah Mitchell, B.Sc. Physics·Updated April 18, 2026
A light ray undergoing Total Internal Reflection inside an optical fibre.

What is the critical angle in physics?

The critical angle is the specific angle of incidence (inside a denser medium like glass or water) that causes the refracted ray to skim exactly along the boundary at 90 degrees. If you increase the angle of incidence even slightly past this point, the light cannot escape and reflects entirely back inside — this is called Total Internal Reflection (TIR).

Table of Contents

Light waves are heavily tested in Paper 2. While wavelength and frequency concepts are straightforward, refraction forces you to use trigonometry. This guide, part of our Ultimate O-Level Physics Guide, shows you exactly how to manipulate Snell's Law and avoid the most common diagramming mistake.

1. Snell's Law and the Normal Trap

When light travels from air into a denser medium like glass, it slows down and bends towards the normal. The relationship between the angles is governed by Snell's Law:

n = sin(i) / sin(r)
  • n: Refractive Index (a number usually between 1.3 and 2.4, no units)
  • i: Angle of incidence (in the less dense medium/air)
  • r: Angle of refraction (in the denser medium/glass)
💡 Tutor's Tip
The #1 mistake students make is using the angle between the ray and the GLASS surface. Angles MUST be measured to the normal. If the examiner tells you "the ray strikes the block at 30° to the surface," your angle of incidence `i` is actually 90 - 30 = 60°. That single mistake costs 3 marks on calculations.

2. The Two Rules of Total Internal Reflection (TIR)

When light tries to leave water or glass and enter the air, it speeds up and bends away from the normal. If the angle is steep enough, it gets trapped inside.

Conditions for TIR:

  1. Light must be traveling from a denser medium to a less dense medium (e.g., glass to air).
  2. The angle of incidence must be greater than the critical angle.

We calculate the critical angle using this formula:

sin(c) = 1 / n

3. Worked Exam Question (The Glass Block)

Question:

A piece of glass has a refractive index of 1.52. A light ray traveling inside the glass strikes the boundary with air at an angle of incidence of 45°. Determine if the light ray will exit the glass, and support your answer with a calculation.

Step 1 — Calculate the Critical Angle

sin(c) = 1 / n
sin(c) = 1 / 1.52 = 0.6578
c = sin⁻¹(0.6578) = 41.1°

Step 2 — Compare to the Angle of Incidence

The ray hits the boundary at an angle of 45°.
Since 45° is greater than the critical angle of 41.1°, TIR occurs.

Step 3 — Write the Conclusion

The light ray will NOT exit the glass. It will undergo Total Internal Reflection.

Sarah Mitchell📋 From the Desk of Sarah Mitchell
Exam hint: Whenever you are asked about optical fibres or endoscopes, the answer is always Total Internal Reflection. Examiners don't want a long essay about light; they are looking for the exact phrase "Total Internal Reflection" (3 words). Write those three words down, get the mark, and move on.

Frequently Asked Questions

What is Snell's Law?▼
Snell's Law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant, known as the refractive index (n = sin i / sin r).
What are the two conditions for Total Internal Reflection?▼
1. Light travels from a denser to a less dense medium. 2. The angle of incidence is greater than the critical angle.
How do you calculate the critical angle?▼
Use the formula sin(c) = 1 / n, where n is the refractive index.
Where are angles of incidence and refraction measured from?▼
They are ALWAYS measured between the light ray and the imaginary Normal line (drawn at 90° to the boundary).

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