College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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refracted angle

### Refraction of Light: Critical Angle Concept **Question:** For what angles θ, is there no refracted ray in the diagram below? #### Diagram Explanation: The diagram shows two regions with different refractive indices: - **Green Region** (top): Refractive index, \( n = 1.1 \) - **Yellow Region** (bottom): Refractive index, \( n = 1.3 \) An incident light ray strikes the boundary between these two regions at an angle \( θ \) relative to the normal (a dashed vertical line). #### Options: 1. ⯀ For only angles greater than 60° 2. ⯀ For only angles greater than 57.8° 3. ⯀ For only angles greater than 45° 4. ⯀ For only angles greater than 32.2° 5. ⯀ For only angles greater than 50.3° To find the specific angle θ where no refracted ray occurs (total internal reflection), one must consider the critical angle. The critical angle can be determined by using Snell's Law: \[ n_1 \sin(θ_c) = n_2 \sin(90^\circ) \] Here, θ_c is the critical angle, \( n_1 \) is the refractive index of the incident medium (yellow region, \( n_1 = 1.3 \)), and \( n_2 \) is the refractive index of the second medium (green region, \( n_2 = 1.1 \)). Solving for θ_c: \[ 1.3 \sin(θ_c) = 1.1 \] \[ \sin(θ_c) = \frac{1.1}{1.3} \] \[ θ_c = \sin^{-1}\left(\frac{1.1}{1.3}\right) \] \[ θ_c ≈ 57.8^\circ \] Thus, for incident angles greater than 57.8°, there will be no refracted ray, indicating total internal reflection. The correct answer is therefore: **For only angles greater than 57.8°**
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Transcribed Image Text:### Refraction of Light: Critical Angle Concept **Question:** For what angles θ, is there no refracted ray in the diagram below? #### Diagram Explanation: The diagram shows two regions with different refractive indices: - **Green Region** (top): Refractive index, \( n = 1.1 \) - **Yellow Region** (bottom): Refractive index, \( n = 1.3 \) An incident light ray strikes the boundary between these two regions at an angle \( θ \) relative to the normal (a dashed vertical line). #### Options: 1. ⯀ For only angles greater than 60° 2. ⯀ For only angles greater than 57.8° 3. ⯀ For only angles greater than 45° 4. ⯀ For only angles greater than 32.2° 5. ⯀ For only angles greater than 50.3° To find the specific angle θ where no refracted ray occurs (total internal reflection), one must consider the critical angle. The critical angle can be determined by using Snell's Law: \[ n_1 \sin(θ_c) = n_2 \sin(90^\circ) \] Here, θ_c is the critical angle, \( n_1 \) is the refractive index of the incident medium (yellow region, \( n_1 = 1.3 \)), and \( n_2 \) is the refractive index of the second medium (green region, \( n_2 = 1.1 \)). Solving for θ_c: \[ 1.3 \sin(θ_c) = 1.1 \] \[ \sin(θ_c) = \frac{1.1}{1.3} \] \[ θ_c = \sin^{-1}\left(\frac{1.1}{1.3}\right) \] \[ θ_c ≈ 57.8^\circ \] Thus, for incident angles greater than 57.8°, there will be no refracted ray, indicating total internal reflection. The correct answer is therefore: **For only angles greater than 57.8°**
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