Revision NotesExam QuestionsPast Papers
International A LevelPhysicsEdexcelRevision Notes2. Waves & ElectricityRefraction, Reflection & PolarisationCritical Angle

Critical Angle (Edexcel International A Level Physics)

Revision Note

Lindsay Gilmour

Last updated

Critical Angle

  • As the angle of incidence at the boundary between a more dense and a less dense medium 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 (if the boundary is straight)

    • At this point, the angle of incidence is known as the critical angle C

    • This can only occur when light passes from a more dense to a less dense material

  • This angle can be found using the formula:

  • This can easily be derived from Snell’s law:

n1 sin θ1 = n2 sin θ2

  • Where:

    • θ1 = C 

    • θ2 = 90°

    • n1  = n

    • 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. The refractive index of the glass cube is 1.45 and the refractive index of the liquid is 1.32.

Total Internal Reflection Worked Example (1), downloadable AS & A Level Physics revision notes

a) Complete the diagram to show the path of the ray beyond X

b) Calculate the critical angle for the ray at the glass-liquid boundary

Answer:

Part (a)

Complete the diagram to show the path of the ray beyond X

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

 Part (b)

Calculate the critical angle for the ray at the glass-liquid boundary:

Step 1: Recall Snell's Law and rearrange to make critical angle the subject

n1 sin θ1 = n2 sin θ2 

sin open parentheses C close parentheses space equals space n subscript 2 over n subscript 1 sin open parentheses theta subscript 2 close parentheses

Step 2: Substitute in the known quantities

  • n1 = refractive index of glass cube = 1.45

  • n2 = refractive index of liquid = 1.32

  • θ1 = C

  • θ2 = 90° (The angle of refraction is 90° when at the critical angle)

sin open parentheses C close parentheses space equals space n subscript 2 over n subscript 1 sin open parentheses theta subscript 2 close parentheses

C space equals space sin to the power of negative 1 end exponent space open parentheses fraction numerator 1.32 over denominator 1.45 end fraction close parentheses space

 

Step 3: Calculate the critical angle

C space equals space 65.55 degree

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'

You've read 0 of your 5 free revision notes this week

Sign up now. It’s free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

    Test yourself

    Did this page help you?

    Previous:Refraction & Refractive IndexNext:Total Internal Reflection
    Lindsay Gilmour

    Author: Lindsay Gilmour

    Expertise: Physics

    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.