Refraction of Light
Refraction is a change in the direction of light rays when they travel from one medium to another. It is the bending of light when it goes through different media.
Angle of Refraction
Light is considered by many scientists to have dual nature, both particle nature and wave nature. First, Particle nature is one in which we consider a stream of packets of energy called photons. Second, Wave nature is considering light as electromagnetic radiation whereas part of it is perceived by humans. Visible spectrum defined by humans lies in a range of 400 to 700 nm wavelengths.
Index of Refraction of Diamond
Diamond, the world’s hardest naturally occurring material and mineral known, is a solid form of the element carbon. The atoms are arranged in a crystal structure called diamond cubic. They exist in a huge variety of colours. Also, they are one of the best conductors of heat and have a very high melting point.
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°**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91195c14-8c67-42a0-b9d0-a3e8c2a59df0%2F4bf0c47e-c217-4620-b713-4797a4cb77c9%2Fbr503r.png&w=3840&q=75)
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