Question

The deepest section of ocean in the world is the Mariana Trench, located in the Pacific Ocean. Here,the ocean floor is as low as 10,918m below the surface. If the index of refraction of water is 1.33, howlong would it take a laser beam to reach the bottom of the treach?

Answer 1

Given:

The depth of the trench, d=10,918 m

The refractive index of the water, n=1.33

To find:

The time it takes for the laser beam to reach the bottom of the ocean.

Step-by-step explanation:

The refractive index of water is given by,

`n=(c)/(v)`

Where c is the velocity of the laser in vacuum and v is the velocity of the laser in water.

On substituting the known values,

`\begin{gathered} 1.33=(3*10^8)/(v) \\ \implies v=(3*10^8)/(1.33) \\ =2.3*10^9\text{ m/s} \end{gathered}`

The velocity is given by the equation,

`v=(d)/(t)`

Where t is the time it takes for the laser to reach the bottom of the trench.

On substituting the known values,

`\begin{gathered} 2.3*10^8=(10,918)/(t) \\ \implies t=(10,918)/(2.3*10^8) \\ =47.5*10^(-6)\text{ s} \\ =47.5\text{ }\mu\text{s} \end{gathered}`

Final answer:

The laser beam would reach the bottom in 47.5 μs