Calculate how thick an absorber needs to be to absorb 25% of the incoming light
using the Lambert-Beer law for absorption. How is the small gain coefficient k of a
laser defined in relation to the absorption coefficient ƒÑƒ¯
To calculate the thickness of an absorber needed to absorb a certain percentage of incoming light, we can use the Lambert-Beer law for absorption. The Lambert-Beer Law describes the relationship between the intensity of light passing through a material and the concentration of the absorbing species within that material. The law is given by the equation:
A = ε * c * d
where:
A is the absorbance,
ε is the molar absorptivity (absorption coefficient) of the substance,
c is the concentration of the absorbing species, and
d is the path length (thickness) of the material.
In this case, you want to find the thickness of the absorber needed to absorb 25% of the incoming light, so the absorbance (A) would be equal to -log(0.25) = 0.602.
The small gain coefficient (k) of a laser is defined in relation to the absorption coefficient (α) as:
k = 2α
Therefore, the absorption coefficient (α) is given by:
α = k / 2
Now, let's calculate the thickness of the absorber using the Lambert-Beer law:
0.602 = ε * c * d
Since you want to find the thickness (d), rearrange the equation:
d = 0.602 / (ε * c)
Note that the calculation of the thickness requires information about the molar absorptivity (ε) and the concentration (c) of the absorbing species in the material. Please provide these values to calculate the exact thickness.