Discussion
Velocity of light in air is \(3 \times 10^{8}\) m/s. Velocity of light in a medium having relative permittivity 3 and relative permeability 2 is ........ .
Answer: A
The velocity is \(\sqrt{\frac{3}{2}} \times 10^{8}\) m/s.
The speed of light in a medium is \(v = \frac{c}{\sqrt{\epsilon_{r}\mu_{r}}}\):
\[ \begin{aligned} v &= \frac{3 \times 10^{8}}{\sqrt{3 \times 2}} \\ &= \frac{3}{\sqrt{6}} \times 10^{8} = \sqrt{\frac{9}{6}} \times 10^{8} \\ &= \sqrt{\frac{3}{2}} \times 10^{8}\ \text{m/s} \end{aligned} \]
That is about \(1.22 \times 10^{8}\) m/s, a refractive index of \(\sqrt{6} \approx 2.45\). The option \(\sqrt{2} \times 10^{8}\) uses only one of the two factors, and the forms with \(\sqrt{3}\) in the numerator invert part of the expression.
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