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

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°