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The deepest section of ocean in the world is the Marianas Trench, located in the...

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andrewmezzo | Student, College Freshman | Valedictorian

Posted May 11, 2013 at 5:12 PM via web

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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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ncchemist | eNotes Employee

Posted May 11, 2013 at 8:23 PM (Answer #1)

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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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