The refractive index of fused quartz is  1.46 and sapphire is 1.77. If the speed of light in quartz is V_q, and in sapphire is V_s then which of the following relation is correct?

The refractive index of a media:

$\mathrm{\mu }=\frac{\mathrm{Speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{vacuum}\left(\mathrm{C}\right)}{\mathrm{Speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{medium} \left({\mathrm{v}}_{\mathrm{medium}}\right)}$

$\Rightarrow {\mathrm{v}}_{\mathrm{medium}}=\frac{\mathrm{Speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{vacuum}\left(\mathrm{C}\right)}{\mathrm{Refractive} \mathrm{index} \left(\mathrm{\mu }\right)}$

The refractive index is inversely related to the speed of light in a medium. The lower the refractive index, the more the speed of light, and vice versa.

The refractive index of quartz is less than the refractive index of sapphire.
 ${\mu }_q < {\mu }_s$
$\Rightarrow {\mathrm{V}}_{\mathrm{q}} > {\mathrm{V}}_{\mathrm{s}}$

Therefore, the speed of light in quartz will be more than the speed of light in sapphire.