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Edexcel A Level (IAL) Physics-2.15 Total Internal Reflection- Study Notes- New Syllabus

Edexcel A Level (IAL) Physics -2.15 Total Internal Reflection- Study Notes- New syllabus

Edexcel A Level (IAL) Physics -2.15 Total Internal Reflection- Study Notes -Edexcel A level Physics – per latest Syllabus.

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Predicting Whether Total Internal Reflection Will Occur

Total Internal Reflection (TIR) is a phenomenon that occurs when a wave (usually light) reflects completely back into a denser medium instead of refracting into a less dense medium. To determine whether TIR will occur, two key conditions must be satisfied.

 Conditions for Total Internal Reflection

TIR occurs only when both of the following are true:

  • Condition 1: The wave must travel from a medium with higher refractive index to one with lower refractive index.
    i.e., \( n_{\text{incident}} > n_{\text{refracted}} \)
  • Condition 2: The angle of incidence must be greater than the critical angle \( C \).

The critical angle is given by:

$ \sin C = \frac{1}{n} $

How to Predict TIR Step-by-Step

  1. Identify which medium is denser (higher refractive index).
  2. Check if the wave is travelling from higher \( n \) → lower \( n \).
    If not → TIR cannot occur.
  3. Calculate the critical angle using:

    $ C = \sin^{-1}\left(\frac{1}{n}\right) $

    (Assuming the other medium is air; if not, use Snell’s law).

  4. Compare the incident angle \( \theta_i \) to the critical angle.
    • If \( \theta_i < C \) → refraction occurs.
    • If \( \theta_i = C \) → refracted ray grazes the boundary.
    • If \( \theta_i > C \) → total internal reflection occurs.

Visual Summary

  • If light enters a denser medium →  No TIR possible.
  • If light leaves a denser medium but \( \theta_i < C \) →  Refraction + partial reflection.
  • If light leaves a denser medium and \( \theta_i > C \) →  100% reflection (TIR).

Example (Easy)

Light travels from glass (\( n = 1.50 \)) to air. Incident angle = \( 20^\circ \). Will total internal reflection occur?

▶️ Answer / Explanation

Step 1: Calculate critical angle:

$ \sin C = \frac{1}{1.50} = 0.667 $ $ C = \sin^{-1}(0.667) \approx 41.8^\circ $

Step 2: Compare angles:

  • Incident angle = \( 20^\circ \)
  • Critical angle = \( 42^\circ \)

Since \( 20^\circ < 42^\circ \), no TIR occurs.

Example (Medium)

A ray in diamond (\( n = 2.42 \)) strikes the boundary with air at \( 30^\circ \). Predict whether TIR occurs.

▶️ Answer / Explanation

Step 1: Find critical angle.

$ \sin C = \frac{1}{2.42} = 0.413 $ $ C = \sin^{-1}(0.413) \approx 24.4^\circ $

Step 2: Compare angles:

  • Incident angle = \( 30^\circ \)
  • Critical angle = \( 24.4^\circ \)

Since \( 30^\circ > 24.4^\circ \), TIR occurs.

Example (Hard)

A ray passes from glass (\( n_1 = 1.60 \)) into water (\( n_2 = 1.33 \)) with incident angle \( 50^\circ \). Will total internal reflection occur?

▶️ Answer / Explanation

Step 1: Use Snell’s law for critical angle:

$ n_1 \sin C = n_2 \sin 90^\circ = n_2 $ $ \sin C = \frac{1.33}{1.60} = 0.831 $ $ C = \sin^{-1}(0.831) \approx 56.3^\circ $

Step 2: Compare angles:

  • Incident angle = \( 50^\circ \)
  • Critical angle = \( 56.3^\circ \)

Since \( 50^\circ < 56.3^\circ \), TIR does NOT occur.

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