A beam of white light is incident on the surface of a diamond at an angle θa�a.(Figure 1) Since the index of refraction depends on the light's wavelength, the different colors that comprise white light will spread out as they pass through the diamond. The indices of refraction in diamond are nred=2.410�red=2.410 for red light and nblue=2.450�blue=2.450 for blue light. The surrounding air has nair=1.000�air=1.000. Note that the angles in the figure are not to scale.
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.
A beam of white light is incident on the surface of a diamond at an angle θa�a.(Figure 1) Since the index of refraction depends on the light's wavelength, the different colors that comprise white light will spread out as they pass through the diamond. The indices of refraction in diamond are nred=2.410�red=2.410 for red light and nblue=2.450�blue=2.450 for blue light. The surrounding air has nair=1.000�air=1.000. Note that the angles in the figure are not to scale.
![## Part C
**Objective:**
Derive a formula for \(\delta\), the angle between the red and blue refracted rays in the diamond.
**Instructions:**
Express the angle in terms of \(n_{\text{red}}, n_{\text{blue}},\) and \(\theta_a\). Use \(n_{\text{air}} = 1\). Note that any trig function entered in your answer must be followed by an argument in parentheses.
**Formula:**
\[
\delta = \sin^{-1}\left(\frac{\sin\theta_{\text{air}}}{n_{\text{red}}}\right) - \sin^{-1}\left(\frac{\sin\theta_{\text{air}}}{n_{\text{blue}}}\right)
\]
**Interface Elements:**
- **Button Labels:**
- **Submit**: Finalize your answer.
- **Previous Answers**: Review past responses.
**Additional Resources:**
- **Hints:** Access via “View Available Hint(s)" for guidance.
- **Keyboard Shortcuts:** Optimize input efficiency.
- **Undo/Redo/Reset Options:** Easily correct or restart the input process.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d7adbf1-3ca3-4012-a27a-9468e79345de%2F0ab7301c-2193-460b-8423-1d9b80cff512%2Ftdkgypg_processed.png&w=3840&q=75)
Step by step
Solved in 3 steps with 3 images
