Use the speed of electromagnetic waves in a medium

The speed of electromagnetic waves in a medium is $v = \frac{1}{\sqrt{\mu\varepsilon}}$

In terms of relative permeability $\mu_r$ and relative permittivity $\varepsilon_r$, $v = \frac{c}{\sqrt{\mu_r\varepsilon_r}}$

where $c = 3 \times 10^8\ \text{m s}^{-1}$.

Substitute the given values

Given: $v = 1.5 \times 10^8\ \text{m s}^{-1}, \quad \mu_r = 2$

So, $1.5 \times 10^8 = \frac{3 \times 10^8}{\sqrt{2\varepsilon_r}}$

Solve for $\varepsilon_r$

Cancel $10^8$ from both sides: $1.5 = \frac{3}{\sqrt{2\varepsilon_r}}$

Rearranging, $\sqrt{2\varepsilon_r} = \frac{3}{1.5} = 2$

Squaring both sides, $2\varepsilon_r = 4$

Hence, $\varepsilon_r = 2$

Match with the options

$\varepsilon_r = 2$

So the correct option is C.