Overview
This lecture explains the concept of total internal reflection, the critical angle, and how these principles apply to materials like water and fiber-optic cables.
Refraction and Mediums
- When light moves from a slow medium (high refractive index) to a fast medium (low refractive index), the angle of refraction increases.
- The angle of refraction (theta 2) is always greater than the angle of incidence (theta 1) in this situation.
Total Internal Reflection
- If the incident angle exceeds a certain value, called the critical angle, light will not refract into the fast medium but reflect back into the slow medium.
- At the critical angle, the refracted light travels exactly along the boundary (angle of refraction is 90 degrees).
- For incident angles larger than the critical angle, total internal reflection occurs.
Calculating the Critical Angle
- Use Snell’s Law: n₁·sin(θ₁) = n₂·sin(θ₂), where n₁ and n₂ are refractive indices.
- For the critical angle, set θ₂ = 90°, so sin(90°) = 1.
- Example: For water (n = 1.33) to air (n = 1.00), sin(θ_c) = 1 / 1.33.
- The critical angle θ_c = inverse sine (1 / 1.33) ≈ 48.8°.
Applications: Fiber-Optic Cables
- Fiber-optic cables use total internal reflection to trap light within a glass tube so signals can travel long distances.
- Incident angles inside the fiber are kept larger than the critical angle to ensure continued reflection.
Key Terms & Definitions
- Angle of Incidence — Angle at which light hits the boundary between two media.
- Angle of Refraction — Angle at which light passes into the second medium.
- Critical Angle — Minimum angle of incidence at which total internal reflection occurs.
- Total Internal Reflection — Complete reflection of light back into a medium when the incident angle exceeds the critical angle.
- Snell’s Law — Formula relating angles of incidence and refraction to refractive indices.
Action Items / Next Steps
- Practice calculating critical angles for different media using Snell’s Law.
- Review how fiber-optic cables utilize total internal reflection.
- Prepare examples for homework on total internal reflection and real-world applications.