Solved Examples of Total Internal Reflection Problems

📚 Quick Study Guide

• 🔍 Total Internal Reflection (TIR) occurs when light traveling from a denser medium to a rarer medium strikes the interface at an angle greater than the critical angle.
• 💡 The critical angle ($\theta_c$) is the angle of incidence for which the angle of refraction is 90 degrees.
• 📝 Snell's Law: $n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$, where $n_1$ and $n_2$ are the refractive indices of the two media, and $\theta_1$ and $\theta_2$ are the angles of incidence and refraction, respectively.
• ➗ Critical Angle Formula: $\theta_c = \sin^{-1}(\frac{n_2}{n_1})$, where $n_1 > n_2$.
• 🌈 TIR Applications: Fiber optics, prisms, and the shimmering appearance of mirages.

🧪 Practice Quiz

1. A light ray travels from water ($n = 1.33$) into air ($n = 1.00$). What is the critical angle for total internal reflection?
   1. 35.0°
   2. 48.8°
   3. 62.5°
   4. 75.0°
2. If the critical angle for a light ray traveling from glass to air is 42°, what is the refractive index of the glass?
   1. 1.25
   2. 1.33
   3. 1.49
   4. 1.65
3. A light ray is incident on a glass-water interface at an angle of 30° from the glass side. The refractive indices of glass and water are 1.5 and 1.33, respectively. Will total internal reflection occur?
   1. Yes
   2. No
   3. Cannot be determined
   4. Only if the angle is greater than 45°
4. What happens to the intensity of the reflected light during total internal reflection?
   1. It decreases
   2. It increases
   3. It remains the same
   4. It becomes zero
5. A fiber optic cable uses total internal reflection to transmit light. If the refractive index of the core is 1.6 and the cladding is 1.4, what is the critical angle?
   1. 50.2°
   2. 61.0°
   3. 72.5°
   4. 81.3°
6. A light ray in a diamond ($n = 2.42$) is incident on a diamond-air interface. What is the critical angle for total internal reflection?
   1. 14.4°
   2. 24.4°
   3. 34.4°
   4. 44.4°
7. Which of the following applications directly uses the principle of total internal reflection?
   1. Microscopes
   2. Telescopes
   3. Fiber optic communication
   4. Cameras