Wave Optics.

Q. Wave Optics.

Question

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 

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.