The deepest section of ocean in the world is the Marianas Trench, located in the Pacific Ocean. Here the ocean floor is as low as 10,918 m below the surface. The index of refraction of water is...

The deepest section of ocean in the world is the Marianas Trench, located in the Pacific Ocean. Here the ocean floor is as low as 10,918 m below the surface. The index of refraction of water is 1.33. Calculate the time for the laser beam to reach the bottom of the trench .

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The refractive index of a medium is a measure of how it affects the speed of light passing through it.  Mathematically, it is defined as:

n = c/v

where n is the refractive index, c is the speed of light in a vacuum, and v is the speed of light in the medium.  Please note that the refractive index is a dimensionless number.  The value of c is a constant (2.99 x 10^8 m/s), so we can use the equation to find the speed of light through water.

1.33 = [2.99 x 10^8 m/s]/v

v = [2.99 x 10^8 m/s]/1.33 = 2.25 x 10^8 m/s

As expected, the speed of light through water is slower than in a vacuum.  Now we can use the speed of light through water and the depth of the ocean to calculate the time.

10,918 m * (1 sec/2.25 x 10^8 m) = 4.85 x 10^-5 seconds

So it takes 0.0000485 seconds for a laser beam to reach the bottom of the Marianas Trench.

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