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.
In the diagram:
- \(r\) is the angle of refraction.
- \(90° - r\) is the complementary angle to \(r\).
- The light enters the prism and undergoes refraction at the first interface, bends towards the normal due to the higher refractive index of the prism, and then travels through the prism.
The task is to determine the second angle of incidence (\(\angle i_s\)) after the light exits the prism.
Apply Snell's Law at the first interface:
\[ n_{\text{air}} \sin i = n_{\text{prism}} \sin r \]
\[ 1 \cdot \sin 45° = 1.6 \cdot \sin r \]
\[ \sin r = \frac{\sin 45°}{1.6} \]
\[ \sin r = \frac{\frac{\sqrt{2}}{2}}{1.6} \approx 0.442 \]
Now, calculate \(r\):
\[ r = \arcsin(0.442) \approx 26.2° \]
Using the geometry of the prism and its internal angles:
\[ \text{Angle at the second interface can be found as} \]
\[ \text{A} = 60° (apex angle) \]
From the geometry of the prism:
\[ \angle i_s = 60° - r \]
\[ \angle i_s = 60° - 26.2° \approx 33.8° \approx 34° \]
**Therefore, the second angle of incidence (\(\angle i_s\)) is approximately 34°.**
### Answer Choices
- 34° \( \text{(Correct Answer)} \)
- 24°
- 19°
- 60°](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0fcb0af8-b750-4635-b3ee-2f0c31e9ebdb%2F488b2f11-d7f2-40bb-a0d1-3fce43bfdd07%2F3w7k887_processed.png&w=3840&q=75)
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