A LevelPhysicsOCRRevision Notes4. Electrons, Waves & PhotonsRefraction & ReflectionTotal Internal Reflection

Total Internal Reflection (OCR A Level Physics): Revision Note

Exam code: H556

Written by: Katie M

Reviewed by: Caroline Carroll

Updated on 2 July 2026

Total Internal Reflection

As the angle of incidence is increased, the angle of refraction also increases until it gets closer to 90°
When the angle of refraction is exactly 90° the light is refracted along the boundary
- At this point, the angle of incidence is known as the critical angle C
This angle can be found using the formula:

This can easily be derived from Snell’s law where:
- θ₁ = C
- θ₂ = 90°
- n₁ = n
- n₂ = 1 (air)

Total internal reflection (TIR) occurs when:
The angle of incidence is greater than the critical angle and the incident refractive index n₁ is greater than the refractive index of the material at the boundary n₂
Therefore, the two conditions for total internal reflection are:
- The angle of incidence, θ₁ > the critical angle, C
- Refractive index n₁ > refractive index n₂ (air)

Total Internal Reflection, downloadable AS & A Level Physics revision notes

Worked Example

A glass cube is held in contact with a liquid and a light ray is directed at a vertical face of the cube. The angle of incidence at the vertical face is 39° and the angle of refraction is 25° as shown in the diagram. The light ray is totally internally reflected at X.

Complete the diagram to show the path of the ray beyond X to the air and calculate the critical angle for the glass-liquid boundary.

Answer:

Total Internal Reflection Worked Example (2), downloadable AS & A Level Physics revision notes

Step 1: Draw the reflected angle at the glass-liquid boundary

When a light ray is reflected, the angle of incidence = angle of reflection
Therefore, the angle of incidence (and reflection) is 90° – 25° = 65°

Step 2: Draw the refracted angle at the glass-air boundary

At the glass-air boundary, the light ray refracts away from the normal
Due to the reflection, the light rays are symmetrical to the other side

Step 3: Calculate the critical angle

The question states the ray is “totally internally reflected for the first time” meaning that this is the lowest angle at which TIR occurs
Therefore, 65° is the critical angle

Examiner Tips and Tricks

Always draw ray diagrams with a ruler, and make sure you're comfortable calculating unknown angles. The main rules to remember are:

Angles in a right angle add up to 90°
Angles on a straight line add up to 180°
Angles in any triangle add up to 180°

For angles in parallel lines, such as alternate and opposite angles, take a look at the OCR GCSE maths revision notes '7.1.1 Angles in Parallel Lines'

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