Discussion
The velocity of light in a medium of relative permittivity 2 and relative permeability 4.5 is (velocity of light in free space is c )
Answer: C
The velocity is \(\frac{c}{3}\).
The speed of light in a medium is
\[ \begin{aligned} v &= \frac{c}{\sqrt{\mu_{r}\varepsilon_{r}}} \\ &= \frac{c}{\sqrt{2 \times 4.5}} \\ &= \frac{c}{\sqrt{9}} \\ &= \frac{c}{3} \end{aligned} \]
\(\frac{c}{\sqrt{3}}\) and \(\frac{c}{2}\) come from using one of the two quantities alone, and \(\frac{c}{4}\) has no basis.
The refractive index of this medium is therefore \(n = \sqrt{\mu_{r}\varepsilon_{r}} = 3\).
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