Question

the speed of light in an unknown medium is measured to be 2.76 x 108 m/s/. what is the index of refraction of the medium?

Answer 1

Answer:

Approximately $1.09$.

Explanation:

Let $c$ denote the speed of light in vacuum: $c \approx 2.9979 \times 10^{8}\; {\rm m \cdot s^{-1}}$.

If the speed of light in a medium is $v$, the refractive index of that medium would be $n = c / v$.

The speed of light in no medium is known to exceed the speed of light in vacuum. In other words, $v \le c$ for all medium. Therefore, the value of the refractive index $n$ should be at least $1$.

In this question, $v = 2.76 \times 10^{8}\; {\rm m \cdot s^{-1}}$ for this medium. The value of the refractive index of this medium would be:

$\begin{aligned}n &= \frac{c}{v} \\ &= \frac{2.76 \times 10^{8}\; {\rm m \cdot s^{-1}}}{2.9979 \times 10^{8}\; {\rm m\cdot s^{-1}}} \\ &\approx 1.09 \end{aligned}$.