🌟 Total Internal Reflection (TIR)
1 🔍 Quick Refresher on Refraction
Light slows down (and bends) when it moves from one material to another. The refractive index tells us “how much slower.” For two media 1 and 2, the indices obey \( n_{21}\,n_{12}=1 \) (Equation 9.11) :contentReference[oaicite:14]{index=14}.
- Optical density (decided by light-speed) can differ from mass density—turpentine is optically denser than water even though it’s physically lighter! :contentReference[oaicite:15]{index=15}
- A ray through a glass slab emerges parallel to itself but sideways-shifted. The bottom of a water tank looks raised for the same reason. :contentReference[oaicite:16]{index=16}
2 ✨ What Is Total Internal Reflection?
Send a beam from an optically denser material to a rarer one (for example, water → air). As you tilt the beam:
- It first refracts away from the normal (angle r gets bigger). :contentReference[oaicite:17]{index=17}
- At a special critical angle \( i_c \), the refracted ray skims along the surface (r = 90°). :contentReference[oaicite:18]{index=18}
- Go beyond \( i_c \): refraction vanishes; the whole beam bounces back—Total Internal Reflection! 💡 :contentReference[oaicite:19]{index=19}
2.1 📐 Maths Behind TIR
Snell’s law gives the two handy relations:
\[ \sin i_c = n_{21}\tag{9.12} \] :contentReference[oaicite:20]{index=20}\[ n_{12}=\frac{1}{\sin i_c} \] :contentReference[oaicite:21]{index=21}(Here \( n_{21}=n_2/n_1<1 \) because medium 2 is rarer.)
3 📊 Critical Angles You Should Know
| Material (to Air) | Refractive Index | \( i_c \) (degrees) |
|---|---|---|
| Water | 1.33 | 48.8° |
| Crown glass | 1.52 | 41.1° |
| Dense flint glass | 1.62 | 37.3° |
| Diamond 💎 | 2.42 | 24.4° |
(Table 9.1) :contentReference[oaicite:22]{index=22}
4 🧪 DIY Demo (Fun & Safe)
Fill a beaker with slightly milky water, shine a laser pointer sideways, and watch the beam zig-zag as it bounces inside—perfect live TIR! 🌈 Just don’t stare into the beam. :contentReference[oaicite:23]{index=23}
5 🚀 Cool Uses & Natural Appearances
- Right-angle & Porro prisms: flip or turn images by 90°/180° with almost zero loss. Perfect for binoculars! :contentReference[oaicite:24]{index=24}
- Optical fibres: a light pulse bounces thousands of times inside the core, carrying internet data or guiding a doctor’s endoscope. Even bends are okay as long as the bounce angle stays > \( i_c \). 🚑 :contentReference[oaicite:25]{index=25}
- “Light-pipe” toys & lamps: the same fibres make decorative fountains of coloured light. 🎇 :contentReference[oaicite:26]{index=26}
6 🎯 High-Yield NEET Nuggets
- TIR occurs only when light tries to move from denser to rarer medium and \( i \gt i_c \).
- Remember the formula \( \sin i_c = n_{21} \); quick way to compute critical angles.
- Diamond’s tiny \( i_c \) (≈ 24°) explains its brilliant sparkle—a favourite MCQ fact.
- Prisms and optical fibres rely on near-100 % reflection efficiency of TIR (far better than mirrors).
Keep shining and bouncing those rays! ✨
