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.
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
$$e^{-6 a}=0.1 \implies 6 a=-\ln{0.1} = \ln{10} \implies a = \frac16 \ln{10}$$
Therefore
$$I(z) = I(0) e^{-(1/6) \ln{10} z} = I(0) 10^{-z/6}$$