Question

A particular material has an index of refraction of 1.25. What percent of the speed of light in a vacuum is the speed of light in the material?

Answer 1

The percentage of speed of light in vacuum to the speed of light in the said material is 80%

Step-by-step explanation:

The common values of refractive index are between 1 and 2 since nothing can travel faster than the speed of light, therefore, no material has a refractive index lower than 1.

According to the formula
`n=(c)/(v)`

where
`n` is the index of refraction

`c` is the speed of light in vacuum

and
`v` is the speed of light in the material, it can be seen that n and v are inversely proportional which means greater the refractive index lower is the speed of light.

Since we know that speed of light in vacuum is 300,000 km/s using the formula we get,

`v=\frac{c}n}`

`v=(300000)/(1.25)=240,000  km/s`

for finding percentage,

`=(240000)/(300000)*100 = <strong>80` %

Answer 2

80% (Eighty percent)

Step-by-step explanation:

The material has a refractive index (n) of 1.25

Speed of light in a vacuum (c) is 2.99792458 x 10⁸ m/s

We can find the speed of light in the material (v) using the relationship

n = c/v, similarly

v = c/n

therefore v = 2.99792458 x 10⁸ m/s ÷ (1.25) = 239 833 966 m/s

v = 239 833 966 m/s

Therefore the percentage of the speed of light in a vacuum that is the speed of light in the material can be calculated as

(v/c) × 100 = (1/n) × 100 = (1/1.25) × 100 = 0.8 × 100 = 80%

Therefore speed of light in the material (v) is eighty percent of the speed of light in the vacuum (c)