**Problem 6.100:The speed of light in a certain material is 50% of its speed in vacuum. What is the refractive index of this material? **

**Solution:**

Refractive index of a material is defined as the ratio of speed of light in vacuum to the speed of light in that material.

Or, Refractive index = $n\:=\:\frac{speed\:of\:light\:in\:vacuum(c)}{speed\:of\:light\:in\:material(v)}$.

Or $n\:=\:\frac{c}{v}$.

Given that The speed of light in the material $($v$)$ is 50% of its speed in vacuum$($c$)$.

Or, $v\:=\:\frac{50}{100}\times c$.

Or, $v\:=\:\frac{c}{2}$.

Then Refractive index, $n\:=\:\frac{c}{\frac{c}{2}}\:=\:2$.

Therefore refractive index of the material is $2$.