Overview
This lecture explains refraction and the refractive index, including its definition, formulas, and applications in different materials such as glass and water.
Refraction of Light
- Refraction is the bending of light when it passes from one medium to another (e.g., air to glass or water).
- Light bends because its speed changes when moving between materials.
- Light slows down in denser media, causing it to bend towards the normal.
Refractive Index: Definition and Formula
- The refractive index (n) measures how much light slows down in a material.
- Formula: n = c / v, where c is the speed of light in vacuum (≈ 3 × 10⁸ m/s) and v is the speed in the material.
- Refractive index is unitless since it is a ratio.
- A higher refractive index means light travels slower and bends more in that material.
Examples and Calculations
- Glass: n = 3 × 10⁸ / 2 × 10⁸ = 1.5
- Water: Given n = 1.33, speed of light in water = 3 × 10⁸ / 1.33 ≈ 2.25 × 10⁸ m/s
- Glass slows light more than water, as shown by its higher refractive index.
Types of Refractive Index
- Absolute refractive index: First medium is vacuum or air.
- Relative refractive index: Light moves from one material to another (e.g., n₂₁ = speed in medium 1 / speed in medium 2).
Refractive Index Using Angles
- Law: n = sin i / sin r, where i is angle of incidence, r is angle of refraction.
- This formula is often easier to use experimentally than measuring speed.
Refractive Index Relationships
- General formula: n₃₂ = n₃₁ / n₂₁ (refractive index of medium 3 with respect to 2).
- For glass with respect to water: n_gw = n_g / n_w.
- The reciprocal relationship: n_wg = 1 / n_gw.
Practical Application
- Higher refractive index lenses are thinner and more expensive, suitable for high power prescriptions.
Key Terms & Definitions
- Refraction — bending of light when it passes between different media due to speed change.
- Refractive Index (n) — ratio of the speed of light in vacuum to that in a material (n = c / v).
- Absolute Refractive Index — refractive index when the first medium is vacuum or air.
- Relative Refractive Index — refractive index comparing two arbitrary media (n₂₁ = v₁ / v₂).
Action Items / Next Steps
- Memorize refractive index formulas (speed and angle-based).
- Practice calculations using both formulas for glass and water.
- Learn the general and reciprocal refractive index relationships.