Q.93. Wave Optics.

Question 93.

The attenuation coefficient of the muscle is 800 cm^-1, at the wavelength emitted by CO2 laser

(1.06 x 10^-5). Calculate the thickness of the muscle layer that absorbs 90% of the light energy of this laser.

Answer 93.

I / I'= e^ ( - μ x )

where
I = intensity of emergent ray
I' = intensity of original ray
μ = attenuation coefficient
x = thickness

As energy is proportional to intensity, putting given information in this formula noting that 90% is absorbed so 10% remains which means I / I' = 0.10

=>0.1 = e ^ ( - 800 x ), where x = thickness in cm.
=> ln (0.1) = - 800x
=> ln 1 - ln 10 = - 800x
=> x = (ln 10) / 800 = 0.003 cm = 0.03 mm.
[Note: wavelength is not required here.]
Source(s):
Refer to page 9 of the .pdf page in the link which gives the formula that can be used to solve your problem.
http://www.physics.uoguelph.ca/~pgarrett/teaching/PHY-1070/lecture-21.pdf#page=9

LINK to YA!