gen-define-fiber-optic-light-guiding-and-give-one-short-worked-e-804d

Define fiber-optic light guiding and give one short worked example.

# Fiber-Optic Light Guiding **Definition:** Fiber-optic light guiding is the transmission of light through a transparent fiber by **total internal reflection**. Light remains confined within the fiber's core because it reflects at the core-cladding boundary when the angle of incidence exceeds the critical angle. ## Key Principle Light is trapped when: $$\sin \theta_i > \sin \theta_c = \frac{n_2}{n_1}$$ where: - θ_i = angle of incidence at the core-cladding interface - n₁ = refractive index of core (higher) - n₂ = refractive index of cladding (lower) --- ## Worked Example **Problem:** A fiber-optic cable has a core with refractive index n₁ = 1.50 and cladding with n₂ = 1.45. Calculate the critical angle for total internal reflection. **Solution:** Using the critical angle formula: $$\sin \theta_c = \frac{n_2}{n_1} = \frac{1.45}{1.50} = 0.967$$ $$\theta_c = \sin^{-1}(0.967) = 75.2°$$ **Answer:** The critical angle is **75.2°**. Any light ray hitting the core-cladding boundary at an angle greater than 75.2° (measured from the normal) will undergo total internal reflection and remain guided within the fiber.