Question

The index of refraction for a vacuum is 1.00000. The index of refraction for air is 1.00029. 1) Determine the ratio of time required for light to travel through 1000 m of air to the time required for light to travel through 1000 m of vacuum. (Express your answer to six significant figures.)

Answer 1

`(t_(air))/(t_(vaccum))` = 1.00029

Step-by-step explanation:

The refractive index is defined

n = c / v

v = c / n

the speed of light per se wave is constant, so we can use the relations of uniform motion

v = x / t

t = x / v

we substitute

t = x n / c

let's calculate the time

vacuum

t₁ = 1000 1/3 10⁸

t₁ = 3.333333 10⁻⁶ s

air

t₂ = 1000 1.00029 / 3 10⁸

t2 = 3.3343 10⁻⁶ s

the relationship between these times is

t₂ / t₁ = 3.3343 / 3.3333333

t₂ / t₁ = 1.00029