Question

There are fiber optic telephone cables connecting North America and Europe, lying on the bottom of the Atlantic ocean. The wire is 4,500 km long how long and has an index of refraction of 1.5. How long will it take for the signal to cross the ocean? Give your answer in milliseconds.

Answer 1

The time taken is
`t = 0.0225 \ s`

Step-by-step explanation:

From the question we are told that

The length of the wire is
`l = 4500 \ km = 4500000 \ m`

The refractive index is
`n_f = 1.5`

The velocity of the signal is mathematically represented as

`v = (c)/(n_f )`

Where c is the speed of light with value
`c = 3.0 *10^(8) \ m/s`

substituting values

`v = (3.0 *10^(8))/(1.5)`

`v = 2.0*10^(8) \ m/s`

The time taken is mathematically evaluated as

`t = (d)/(v)`

substituting values

`t = (4500000)/(2.0 *10^(8))`

`t = 0.0225 \ s`