Answer
$v_1-v_2=4.55\times 10^7\frac{m}{s}$
Work Step by Step
Speed of light in sapphire is given as:
$v_1=\frac{c}{n_1}$
We plug in the known values to obtain:
$v_1=\frac{3\times 10^8}{1.77}=1.6949\times 10^8\frac{m}{s}$
Speed of light in diamond is given as
$v_2=\frac{c}{n_2}$
We plug in the known values to obtain:
$v_2=\frac{3\times 10^8}{2.42}=1.2397\times 10^8\frac{m}{s}$
The difference of speed and sapphire can be determined as:
$v_1-v_2=1.6949\times 10^8-1.2397\times 10^8=4.55\times 10^7\frac{m}{s}$
