The index of refraction of diamond is $2.0$, velocity of light in diamond in $\text{cm/s}$ is approximately

The correct option is D $1.5\times {10}^{10}$
We know,

Refractive index of diamond is given by,

$=\frac{\text{Velocity of light in air}}{\text{Velocity of light in diamond}}$

$\Rightarrow 2=\frac{3\times {10}^8}{\text{velocity of light in diamond}}$

So, $\text{Velocity of light in diamond}=\frac{3\times {10}^8}{2}=1.5\times {10}^8\text{m/s}$

But we need velocity in $\text{cm/s}$

Therefore, velocity of light in diamond,

$1.5\times {10}^8\times {10}^2$

$1.5\times {10}^{10}\text{cm/s}$