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JEE Physics Focus Reading Time: 14 min 3 Key Concepts

Total Internal Reflection (TIR): From Mirage to Optical Fibers

Master the critical angle condition and its revolutionary applications in everyday life and technology.

3
Key Concepts
100%
JEE Relevance
5+
Applications
18min
Practice Time

Why Total Internal Reflection Matters

Total Internal Reflection (TIR) is not just a theoretical concept but a phenomenon that powers modern technology and creates natural wonders. Understanding TIR is crucial for:

  • Optical fiber communication - backbone of internet
  • Medical endoscopy - non-invasive diagnostics
  • Natural phenomena - mirage, sparkling diamonds
  • JEE problems - direct applications in ray optics
Concept 1 Fundamental

Critical Angle Condition

$$\sin i_c = \frac{n_2}{n_1} \quad \text{where } n_1 > n_2$$

The angle of incidence for which angle of refraction becomes 90°

📐 Derivation from Snell's Law:

Step 1: Start with Snell's Law:

$n_1 \sin i = n_2 \sin r$

Step 2: At critical angle, $r = 90^\circ$:

$n_1 \sin i_c = n_2 \sin 90^\circ$

Step 3: Since $\sin 90^\circ = 1$:

$n_1 \sin i_c = n_2$

Step 4: Final formula:

$\sin i_c = \frac{n_2}{n_1}$

🎯 JEE Application Example:

Problem: Calculate critical angle for glass-air interface ($\mu_{glass} = 1.5$)

Solution: Using the formula:

$\sin i_c = \frac{1}{1.5} = 0.6667$

$i_c = \sin^{-1}(0.6667) \approx 41.8^\circ$

Concept 2 Important

Conditions for Total Internal Reflection

✓ Necessary Conditions:

  • Light must travel from denser to rarer medium
  • Angle of incidence > critical angle
  • $n_1 > n_2$ (Refractive index condition)

✗ When TIR Fails:

  • Rarer to denser medium
  • $i < i_c$ (Refraction occurs)
  • $i = i_c$ (Grazing emergence)

🔍 Visual Understanding:

Case 1: $i < i_c$ → Partial reflection + refraction

Case 2: $i = i_c$ → Refraction along surface

Case 3: $i > i_c$ → Total internal reflection

🌍 Real-World Applications of TIR

Mirage Formation

Natural Phenomenon

Physics Behind Mirage:

Step 1: Temperature gradient creates refractive index gradient

Step 2: Air near ground is hotter → less dense → lower refractive index

Step 3: Light rays from sky bend upward due to continuous refraction

Step 4: At certain point, TIR occurs and rays reach observer's eye

Step 5: Brain interprets as water reflection (virtual image)

Optical Fiber Communication

Technology

Working Principle:

Core: High refractive index glass/plastic

Cladding: Lower refractive index material

Principle: Light undergoes multiple TIR inside core

Advantages: High bandwidth, low loss, immune to EMI

Applications: Internet, telephone, medical endoscopy

Diamond Brilliance

Jewelry

Why Diamonds Sparkle:

High Refractive Index: $\mu_{diamond} = 2.42$

Small Critical Angle: $i_c = \sin^{-1}(\frac{1}{2.42}) \approx 24.4^\circ$

Multiple TIR: Light trapped inside due to careful cutting

Brilliance: Maximum light emerges from top facets

🚀 Problem-Solving Strategies

JEE Exam Tips:

  • Always check $n_1 > n_2$ condition first
  • Remember $\sin i_c = \frac{n_2}{n_1}$ for denser→rarer
  • For prism problems, use geometry with TIR
  • Practice numerical on critical angle calculation

Common Mistakes:

  • Applying TIR for rarer→denser medium
  • Forgetting the $i > i_c$ condition
  • Mixing up refractive indices in formula
  • Ignoring partial reflection in $i < i_c$ case

Advanced Applications Available

Includes prism applications, total reflecting prisms, and JEE Advanced level problems

📝 Quick Self-Test

Try these JEE-level problems to test your understanding:

1. Calculate critical angle for water-air interface ($\mu_{water} = 1.33$)

2. Explain why diamonds have smaller critical angle than glass

3. A light ray enters fiber with $\mu_{core} = 1.62$, $\mu_{clad} = 1.44$. Find maximum acceptance angle

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