Overview
This lecture covers the physics of reflection and refraction, exploring how light interacts with different media, laws governing these behaviors, key equations, and concepts like total internal reflection and dispersion.
Reflection
- Reflection occurs when light strikes a medium and bounces back into the original medium.
- The angle of incidence (incoming angle) equals the angle of reflection (outgoing angle).
- Law of reflection: θ₁ = θ₁' (θ₁ = angle of incidence, θ₁' = angle of reflection).
- Applies to smooth, flat surfaces.
Refraction
- Refraction is the bending of light as it passes from one transparent medium to another.
- The angle of refraction (θ₂) generally differs from the angle of incidence unless the media have identical indices of refraction.
- Only a portion of light is refracted; some may be reflected.
Index of Refraction
- The index of refraction (n) = speed of light in vacuum (c) / speed of light in medium (v).
- n > 1 for all transparent media except vacuum (n = 1 by definition).
- Higher n means light travels slower in that medium.
- Speed of light in air is nearly equal to vacuum; water is n = 1.33, some glass n ≈ 1.52.
Frequency and Wavelength Changes
- When light enters a new medium, frequency remains constant; wavelength and speed change.
- Shorter wavelength and speed in a medium with higher n.
- λ_medium = λ_vacuum / n, where λ is wavelength.
Snell’s Law of Refraction
- Snell’s Law: n₁·sinθ₁ = n₂·sinθ₂.
- n₁ and θ₁: index and angle in the initial medium; n₂ and θ₂: index and angle in the second medium.
- If n₂ > n₁, light bends toward normal (θ₂ < θ₁); if n₂ < n₁, light bends away from normal (θ₂ > θ₁).
Total Internal Reflection
- Occurs when light moves from higher to lower n and angle of incidence exceeds the critical angle.
- No refraction occurs, only reflection within the medium.
- Critical angle: θ_c = sin⁻¹(n₂/n₁), possible only if n₁ > n₂.
- Used in fiber optic cables for efficient light transmission.
Dispersion
- The index of refraction depends on wavelength; shorter wavelengths (blue/violet) have higher n than longer (red).
- Causes white light to separate into different colors when passing through prisms or raindrops (rainbows).
Key Terms & Definitions
- Reflection — When light bounces off a surface back into its original medium.
- Refraction — Bending of light as it passes between media of different densities.
- Index of Refraction (n) — Ratio of light speed in vacuum to that in a medium.
- Snell’s Law — Equation relating angles and indices of refraction across a boundary.
- Total Internal Reflection — Complete reflection within a medium when the incident angle exceeds the critical angle.
- Critical Angle — Minimum angle of incidence for total internal reflection to occur.
- Dispersion — Splitting of light into component wavelengths due to wavelength-dependent index of refraction.
Action Items / Next Steps
- Practice Snell’s law calculations with various media and angles.
- Review example problems involving critical angle and total internal reflection.
- Read about applications of fiber optics and the physics of rainbows.