Question

The speed of light in vacuum is exactly 299,792,458 m/s. A beam of light has a wavelength of 651 nm in vacuum. This light propagates in a liquid whose index of refraction at this wavelength is 1.16. What is the speed of this light in the liquid? Give an answer in 108 m/s. Pay attention to the number of significant figures.

Answer 1

Answer:

$v=2.58\times10^8m/s$

Explanation:

The index of refraction is equal to the speed of light c in vacuum divided by its speed v in a substance, or $n=\frac{c}{v}$. For our case we want to use $v=\frac{c}{n}$, which for our values is equal to:

$v=\frac{c}{n}=\frac{299792458m/s}{1.16}=258441774.138m/s$

Which we will express with 3 significant figures (since a product or quotient must contain the same number of significant figures as the measurement with the  least number of significant figures):

$v=2.58\times10^8m/s$