Answer :
Explanation
The refractive index of a medium (n) is equal to the speed of light (c) divided by the velocity of light through the medium (v)
[tex]\begin{gathered} n=\frac{c}{v} \\ where\text{ n is the index of refraction} \\ \text{c is the speed of ligth in vacuum} \\ v\text{ is the velocity of ligth in the medium} \end{gathered}[/tex]so
Step 1
a) for Diamons
[tex]\begin{gathered} n=\frac{c}{v} \\ 2.42=\frac{c}{v_1} \\ isolate\text{ v}_1 \\ v_1=\frac{c}{2.42} \end{gathered}[/tex]b) fuzed quarts
[tex]\begin{gathered} n=\frac{c}{v} \\ 1.46=\frac{c}{v_2} \\ isolate\text{ v}_2 \\ v_2=\frac{c}{1.46} \end{gathered}[/tex]Step 2
now,compare:
[tex]\begin{gathered} v_{1}=\frac{c}{2.42} \\ v_2=\frac{c}{1.46} \end{gathered}[/tex]due to c is constant, the velocity 2 is greater ( c is divide by a smaller number)
hence, the speed of light in diamonds is ..
a.lower than that in quartz.
I hope this helps you