Advanced Optics
Year 11 (IGCSE) 🌊 Waves & Optics Apply total internal reflection; solve problems with lenses.
💎 Total Internal Reflection
When light travels from a denser medium (e.g. glass) to a less dense medium (e.g. air) at an angle greater than the critical angle (c), it is completely reflected back. No light escapes!
💎 Critical Angle Formula
$$\sin C = \frac{n_2}{n_1} = \frac{1}{n} \quad \text{(when } n_2 = 1 \text{ for air)}$$| 🧊 Condition | 🔦 What happens |
|---|---|
| θ < critical angle | Refraction — light exits (bent away from normal) |
| θ = critical angle | Refracted ray travels along the boundary (90°) |
| θ > critical angle | Total internal reflection — ALL light reflected back in |
💎 Diamond (n = 2.42): sin C = 1/2.42 → C ≈ 24.4°. The very small critical angle means light bounces around inside many times, creating brilliance!
🌐 Applications of Total Internal Reflection
TIR has several important practical applications in modern technology.
| ⚙️ Application | 📝 How TIR is used |
|---|---|
| 🌐 Optical fibres | Light bounces along the fibre without escaping — transmits data (internet) and voice at the speed of light with minimal loss |
| 🏥 Endoscopes | Bundle of optical fibres lets doctors see inside the body without surgery |
| 🔭 Periscopes (prism type) | Glass prisms use TIR at 45° to redirect light (more efficient than mirrors) |
| 💎 Gemstones | Cut to use TIR to maximise internal reflections and sparkle |
🔭 Thin Lens Formula
The thin lens formula connects object distance, image distance, and focal length.
🔭 Lens Formula
$$\frac{1}{v} - \frac{1}{u} = \frac{1}{f} \qquad m = \frac{v}{u}$$
$f$ = focal length (+ for converging, − for diverging)
$u$ = object distance (negative: real object on left)
$v$ = image distance (+ right = real image, − left = virtual)
🔍 Example: Object 30 cm from a converging lens of f = 10 cm. Find image distance.
1/v − 1/(−30) = 1/10 → 1/v = 1/10 − 1/30 = 3/30 − 1/30 = 2/30 → v = 15 cm (real image, on the other side)
1/v − 1/(−30) = 1/10 → 1/v = 1/10 − 1/30 = 3/30 − 1/30 = 2/30 → v = 15 cm (real image, on the other side)
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💎 Critical Angle & Lens Calculator
Snell's Law & Critical Angle