gen-define-the-critical-angle-and-give-one-short-worked-example-16fb

Define the critical angle and give one short worked example.

# Critical Angle ## Definition The **critical angle** is the angle of incidence in the denser medium at which the refracted ray travels along the boundary between two media (angle of refraction = 90°). For angles greater than the critical angle, total internal reflection occurs. The critical angle θc is given by: $$\sin \theta_c = \frac{n_2}{n_1}$$ where n₁ is the refractive index of the denser medium and n₂ is the refractive index of the less dense medium (n₁ > n₂). --- ## Worked Example **Question:** Calculate the critical angle for light traveling from glass (n = 1.5) into air (n = 1.0). **Solution:** Using the critical angle formula: $$\sin \theta_c = \frac{n_2}{n_1} = \frac{1.0}{1.5} = 0.667$$ $$\theta_c = \sin^{-1}(0.667) = 41.8°$$ **Answer:** The critical angle is **41.8°**. This means any light ray hitting the glass-air boundary at an angle greater than 41.8° (from the normal) will be totally internally reflected back into the glass.