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Chapter 21: Problem 7

Compute the velocity of light in diamond, which has a dielectric constant \(\epsilon_{r}\) of \(5.5\) (at frequencies within the visible range) and a magnetic susceptibility of \(-2.17 \times 10^{-5}\)

Short Answer

Expert verified
Answer: The velocity of light in diamond is approximately 1.26 x 10^8 m/s.

Step by step solution

01

Calculate relative permeability (\(\mu_{r}\))

Using the given magnetic susceptibility \(\chi_m = -2.17 \times 10^{-5}\), calculate the relative permeability, \(\mu_{r}\), using the formula: \(\mu_{r} = 1 + \chi_m\) Plug in the value of \(\chi_m\): \(\mu_{r} = 1 - 2.17 \times 10^{-5}\) Calculating the value of \(\mu_{r}\): \(\mu_{r} \approx 0.9999783\)
02

Calculate the velocity of light in diamond

Now, we have the dielectric constant \(\epsilon_{r} = 5.5\) and the relative permeability \(\mu_{r} \approx 0.9999783\). Use the formula for the velocity of light in a medium: Velocity of light in a medium = \(\frac{c}{\sqrt{\epsilon_{r}\cdot\mu_{r}}}\) Plug in the values of \(\epsilon_{r}\), \(\mu_{r}\), and the speed of light in vacuum (c = \(3 \times 10^8 m/s\)): Velocity of light in diamond = \(\frac{3 \times 10^8}{\sqrt{5.5 \cdot 0.9999783}}\) Compute the velocity of light in diamond: Velocity of light in diamond \(\approx 1.26 \times 10^8 m/s\) Thus, the velocity of light in diamond is approximately \(1.26 \times 10^8 m/s\).

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Most popular questions from this chapter

In your own words, describe how a ruby laser operates.

Using the data in Table \(21.1\), estimate the dielectric constants for silica glass (fused silica), soda-lime glass, polytetrafluoroethylene, polyethylene, and polystyrene, and compare these values with those cited in the following table. Briefly explain any discrepancies. \begin{tabular}{lc} \hline Material & Dielectric Constant (1 MHz) \\ \hline Silica glass & \(3.8\) \\ \hline Soda-lime glass & \(6.9\) \\ \hline Polytetrafluoroethylene & \(2.1\) \\ \hline Polyethylene & \(2.3\) \\ \hline Polystyrene & \(2.6\) \\ \hline \end{tabular}

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