Edexcel International A Level Physics

Revision Notes

2.14 Critical Angle

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Critical Angle

  • As the angle of incidence is increased, the angle of refraction also increases until it gets 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°
    • nn
    • n2 = 1 (air)

Worked example

A glass cube is held in contact with a liquid and a light ray is directed at the 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.Total Internal Reflection Worked Example (1), downloadable AS & A Level Physics revision notesComplete the diagram to show the path of the ray beyond X to the air and calculate the critical angle for the glass-liquid boundary.

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

Exam Tip

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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Lindsay Gilmour

Author: Lindsay Gilmour

Lindsay graduated with First Class Honours from the University of Greenwich and earned her Science Communication MSc at Imperial College London. Now with many years’ experience as a Head of Physics and Examiner for A Level and IGCSE Physics (and Biology!), her love of communicating, educating and Physics has brought her to Save My Exams where she hopes to help as many students as possible on their next steps.