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:
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:
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°
Discussion & Comments