Exponential growth/reduction of Laser Intensity question? Hi i have a pretty simple question but I

dglennuo

dglennuo

Answered question

2022-05-26

Exponential growth/reduction of Laser Intensity question?
Hi i have a pretty simple question but I am not quite sure on how to solve/approach it.
THe question: "The Intensity of a laserbeam declines with the penetrationdepth into matter exponentially. At 6mm depth the intensity has been reduced to 10% of the original value.
Formulate the Intensityreduction formula."
I am not quite sure on how to solve this and any hints/helpful nudges would be appreciated.

Answer & Explanation

Bruce Bridges

Bruce Bridges

Beginner2022-05-27Added 13 answers

Generally speaking, write
I ( z ) = I ( 0 ) e a z
We seek a. We get this knowing that
I ( 6 ) = I ( 0 ) e 6 a = 0.1 I ( 0 )
which means that
e 6 a = 0.1 6 a = ln 0.1 = ln 10 a = 1 6 ln 10
Therefore
I ( z ) = I ( 0 ) e ( 1 / 6 ) ln 10 z = I ( 0 ) 10 z / 6

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