Total Internal Reflection – Identifying the critical angle condition Critical angle for electromagnetic radiation at an interface occurs under which angular condition?

Difficulty: Easy

Correct Answer: Angle of refraction equals 90°

Explanation:


Introduction / Context:
Critical angle marks the onset of total internal reflection when light (or EM waves) travels from a denser to a rarer medium. Beyond this, refraction ceases and all energy reflects along with an evanescent field at the boundary.


Given Data / Assumptions:

  • Two homogeneous media with refractive indices n1 > n2.
  • Angles measured from the normal.
  • Snell’s law governs refraction.


Concept / Approach:
Snell’s law: n1 * sin θ_i = n2 * sin θ_t. At the critical angle θ_c, the refracted ray grazes the interface, i.e., θ_t = 90°. Therefore sin θ_c = n2 / n1 (valid only when n1 > n2).


Step-by-Step Solution:
Set θ_t = 90° at critical condition.Apply Snell’s law: n1 * sin θ_c = n2 * sin 90° = n2.Thus sin θ_c = n2 / n1 (requires n1 > n2).


Verification / Alternative check:
For glass (n ≈ 1.5) to air (n ≈ 1.0), sin θ_c ≈ 1/1.5 ≈ 0.667, so θ_c ≈ 41.8°, consistent with experience.


Why Other Options Are Wrong:

  • (a) Reflection equality is unrelated to refraction.
  • (b) True for many incidences but does not define critical angle.
  • (c) Incidence at 90° is not the critical condition.
  • (e) Reflection angle is never 90° for typical incidence on a plane surface.


Common Pitfalls:
Measuring angles from the surface instead of the normal, or applying the formula when n1 ≤ n2, where no critical angle exists.


Final Answer:
Angle of refraction equals 90°

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