Question

What is the speed of light in olive oil? In a diamond?

Answer 1

\[n = \frac{ c }{ v }\]
\[v = \frac{ c }{ n }\]

This is the typical formula we can use in finding the speed, or velocity of light, in a substance other than a vacuum. Here:

- n is the refractive index of the substance
- c is the velocity of light in a vacuum, or commonly what we say its velocity in air is. We usually say this is approximately 3 x 10^8 m/s.
- v is the velocity of light through the substance we are referring to (olive oil, diamond, etc...)

So, given that c will stay constant in any calculation, then all we need to know is the refractive index of the substance, n. In any question you do on light or optics, if you do not have to find n it should usually be given to you, as it is a constant for the substance itself. The refractive index of diamond is 2.417, for example, so to work out v through diamond we would calculate:

\[v = \frac{ c }{ n } = \frac{ 3 \times 10^{8} m/s}{ 2.417 }\]
to get the answer (in m/s). I'm not sure of the refractive index of olive oil, but I'd say you'll find it somewhere online...if you look hard enough! Anyway, to find the speed of light through this would be the exact same process as that of the diamond, simply subbing in the refractive index of olive oil and working it out. Hope that helps!! :)

Answer 2

Thank you!!

Answer 3

No problem @Me16 !