100 lumen of light are incident on an interface which has 25% reflectance. At a point 3cm into the new medium, the amount of transmitted light is measured as 50 lumen. What is the absorptance of the material per cm?
0.75 * exp(-k*L) = 50/100 = 0.5
L = 3 cm
The 0.75 is the fraction that penetrates the surface.
Solve for k
exp(-kL) = 0.667
kL = 0.4055
k = 0.135 cm^-1
To find the absorptance of the material per cm, we need to calculate the transmittance and reflectance first.
Transmittance (T) is the ratio of transmitted light to the incident light. Since the transmitted light is measured as 50 lumen and the incident light is 100 lumen, we can calculate the transmittance as:
T = Transmitted light / Incident light = 50 / 100 = 0.5
Reflectance (R) is the ratio of reflected light to the incident light. The given information tells us that the interface has a reflectance of 25%. Therefore, the reflectance can be calculated as:
R = Reflectance = 25% = 0.25
Now, the absorptance (A) is defined as the fraction of light that is absorbed by the material. Since the sum of transmittance, reflectance, and absorptance is equal to 1, we can calculate the absorptance by subtracting the sum of transmittance and reflectance from 1:
A = 1 - (T + R) = 1 - (0.5 + 0.25) = 1 - 0.75 = 0.25
The absorptance of the material per cm is 0.25, or 25%.