Find the speed of light through an emerald. The index of refraction for an emerald is 1.58. Use the 3.00 x 108 m S formula: n = speed of light in a medium
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.
![**Educational Website Content:**
**Topic: Refraction and Speed of Light through Different Mediums**
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**Question 4: Finding the Speed of Light through an Emerald**
To determine the speed of light as it travels through an emerald, we can utilize the concept of the index of refraction. An emerald has an index of refraction, \( n \), of 1.58. The formula to calculate the speed of light in a material is given by:
\[ n = \frac{3.00 \times 10^8 \frac{m}{s}}{\text{speed of light in a medium}} \]
Where:
- \( 3.00 \times 10^8 \, \frac{m}{s} \) represents the speed of light in a vacuum.
- The index of refraction \( n \) is a dimensionless number that describes how much the light slows down in the medium compared to its speed in a vacuum.
**Options:**
1. \( 3.00 \times 10^8 \, \frac{m}{s} \)
2. \( 1.58 \times 10^8 \, \frac{m}{s} \)
3. \( 4.74 \times 10^8 \, \frac{m}{s} \)
4. \( 1.90 \times 10^8 \, \frac{m}{s} \)
**Explanation:**
Let's use the formula:
\[ n = \frac{c}{v} \]
Where:
- \( c = 3.00 \times 10^8 \, \frac{m}{s} \) (speed of light in vacuum)
- \( v = \text{speed of light in the material} \)
Given \( n = 1.58 \):
\[ 1.58 = \frac{3.00 \times 10^8 \, \frac{m}{s}}{v} \]
Solving for \( v \):
\[ v = \frac{3.00 \times 10^8 \, \frac{m}{s}}{1.58} \]
\[ v \approx 1.90 \times 10^8 \, \frac{m}{s} \]
Therefore, the correct answer is:
**Option 4: \( 1.90 \times 10^8 \, \frac{](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F098f8e04-469a-4a6a-8094-b45e233f0633%2Fadbe96bd-404c-41ee-aa2d-4c0d269f5246%2F54buihi_processed.jpeg&w=3840&q=75)
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