Solved Examples of Total Internal Reflection and Critical Angle

📚 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 governs refraction: $n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$, where $n$ is the refractive index and $\theta$ is the angle.
• 📐 To find the critical angle, use: $\theta_c = \sin^{-1}(\frac{n_2}{n_1})$, where $n_1 > n_2$.
• 🌈 TIR is used in optical fibers, binoculars, and endoscopes.
• 🧪 TIR only happens when light travels from a higher refractive index to a lower refractive index (e.g., glass to air).

Practice Quiz

1. Question 1: Light travels from water ($n = 1.33$) to air ($n = 1.00$). What is the critical angle?
   1. 35.0°
   2. 48.8°
   3. 62.5°
   4. 75.0°
2. Question 2: What condition is necessary for total internal reflection to occur?
   1. Light travels from a rarer to a denser medium.
   2. The angle of incidence is less than the critical angle.
   3. Light travels from a denser to a rarer medium and the angle of incidence is greater than the critical angle.
   4. The angle of refraction is 0°.
3. Question 3: A light ray in glass ($n = 1.50$) is incident on a glass-air interface at an angle of 40°. Given that the critical angle is approximately 41.8°, what happens to the light ray?
   1. It is completely reflected.
   2. It is partially reflected and partially refracted.
   3. It is completely refracted.
   4. It undergoes diffraction.
4. Question 4: Which of the following applications directly utilizes total internal reflection?
   1. Microscopes
   2. Telescopes
   3. Optical fibers
   4. Cameras
5. Question 5: The critical angle for a certain substance in air is 45°. What is the refractive index of the substance?
   1. 0.707
   2. 1.00
   3. 1.414
   4. 1.50
6. Question 6: Light is incident on a boundary between two materials. Total internal reflection is observed. What can you say about the refractive indices $n_1$ and $n_2$ of the two materials?
   1. $n_1 < n_2$
   2. $n_1 = n_2$
   3. $n_1 > n_2$
   4. The relationship depends on the angle of incidence.
7. Question 7: If the refractive index of diamond is 2.42, what is its critical angle with air?
   1. 24.4°
   2. 35.0°
   3. 41.1°
   4. 52.2°