Explanation

(d) Given refractive index
$n = 1.5$
Permeability $\mu_{0} = \ 5\ \times \ 10^{- 7}\ $
$n = \sqrt{\mu_{r}\varepsilon_{r}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \varepsilon_{r} = \frac{n^{2}}{\mu_{r}}$
or $\rho\ = \ \frac{n^{2}\mu_{0}}{\mu}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left( \because\mu_{r} = \frac{\mu}{\mu_{0}} \right)\ $
or $\varepsilon_{r} = \frac{{(1.5)}^{2}\ \times \ 4\pi\ \times \ 10^{- 7}}{5\ \times \ 10^{- 7}}$
or $\varepsilon_{r} = 6$