Speed of light in a material medium is given by $frac{c}{n}$, where $c$ is the speed of light in vacuum and $n$ is the refractive index of the medium. Now since the refractive index diamond is greater than water, the speed of light is less in diamond than water.

So the speed of the light in that medium is

$$
v=frac{d}{t}=frac{1.56 {rm m}}{6.76times10^{-9} {rm s}}=2.30times10^{8} {rm m/s}
$$

Speed of light in vacuum is $c=3times10^{8} {rm m}$.

Hence refractive index is

$$
n=frac{c}{v}=frac{3times10^{8} {rm m/s}}{2.30times10^{8} {rm m/s}}=1.30
$$