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Chapter 22: Problem 14

What is the speed of light in a diamond that has an index of refraction of \(2.4168 ?\)

Short Answer

Expert verified
Answer: The speed of light in a diamond with an index of refraction of 2.4168 is approximately \(1.24 \times 10^8~m/s\).

Step by step solution

01

Understand the Formula and Given Information

The formula to find the speed of light in a medium is: \(v = \frac{c}{n}\), where \(v\) is the speed of light in the medium, \(c\) is the speed of light in a vacuum, and \(n\) is the index of refraction of the medium. We know that the speed of light in a vacuum, \(c = 3.00\times10^8~m/s\), and the index of refraction of the diamond, \(n = 2.4168\).
02

Calculate the Speed of Light in Diamond

Using the formula, plug in the given values to find the speed of light in the diamond: \(v = \frac{c}{n} = \frac{3.00\times10^8~m/s}{2.4168}\) Now, we perform the calculation: \(v ≈ 1.24 \times 10^8~m/s\)
03

Write the Final Answer

The speed of light in a diamond with an index of refraction of \(2.4168\) is approximately \(1.24 \times 10^8~m/s\).

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