Light is shone on a 1.0 µm thick film of a material with an absorption coefficient of 1.0×10⁴ cm⁻¹. Which value is closest to the fraction of light transmitted through the film? Neglect surface reflection and take I = I₀exp(−αx).

Answer: A. About 37%

Converting the thickness to cm gives x = 1.0 µm = 1.0×10⁻⁴ cm, so αx = 1.0×10⁴ × 1.0×10⁻⁴ = 1.0. The transmitted fraction is exp(−1.0) ≈ 0.37, about 37%. About 10% calculates with a power of ten (10⁻¹) instead of exp, confusing this with absorbance defined by the common logarithm. About 63% is 1 − exp(−1), the fraction absorbed in the film. 1/α is the penetration depth at which the light intensity falls to 1/e, here 1 µm. Direct-gap semiconductors have large α of 10⁴–10⁵ cm⁻¹ for light with energy above the band gap, so even thin films absorb light sufficiently.