You turn on a flashlight in a dark room and observe the light going from the flashlight and through a clear liquid at 3.1 × 10^7 m/s. What is the index of refraction of the clear liquid?

Question

You turn on a flashlight in a dark room and observe the light going from the flashlight and through a clear liquid at 3.1 × 10^7 m/s. What is the index of refraction of the clear liquid?

Answer 1

Index of refraction (n is the common symbol) is the ratio of the speed of light in a vacuum (c) over the speed of light in a given material (v). So n=c/v.

In this case n = 3*10⁸m/s / 3.1*10⁷m/s = 9.7

The units cancel out and you are left with a dimensionless number, which is kind of weird.

Remember that this index will describe the degree to which light bends or refracts when it goes from one material to another. This is why a straw in a glass of water often appears broken.

Answer 2

The Index of Refraction of a medium can be defined as n = c / v, where c is the speed of light in a vacuum and v is the speed of light in the medium. The speed of light in a vacuum is 2.998 x 10⁸ m/s, and we can plug this and our given speed through the liquid into the equation above. n = (2.998 x 10⁸ m/s) / (3.1 x 10⁷ m/s) = 9.671. We are given 2 significant figures for the speed in the liquid, and so we should report our answer as 9.7.