Which formula expresses absorbance from percent transmittance?

Which formula expresses absorbance from percent transmittance?

• A. 1 - log(%T)
• B. log(%T)/2
• C. 2 x log(%T)
• D. 2 - log(%T)

Answer: (D)

Absorbance comes from how much light is blocked, and it relates to transmittance by a logarithm: A = -log10(T), where T is the transmitted fraction (0 to 1). When you’re given percent transmittance, %T, you first turn it into a fraction: T = %T/100. Plugging that in gives A = -log10(%T/100) = -log10(%T) + log10(100) = 2 - log10(%T). So absorbance equals two minus the common logarithm of the percent transmittance. For example, if %T = 50, A ≈ 2 - 1.699 = 0.301, illustrating how lower %T yields higher absorbance. The other forms don’t match this relationship because they omit the division by 100 inside the log or otherwise alter the constant.

Absorbance comes from how much light is blocked, and it relates to transmittance by a logarithm: A = -log10(T), where T is the transmitted fraction (0 to 1). When you’re given percent transmittance, %T, you first turn it into a fraction: T = %T/100. Plugging that in gives A = -log10(%T/100) = -log10(%T) + log10(100) = 2 - log10(%T). So absorbance equals two minus the common logarithm of the percent transmittance. For example, if %T = 50, A ≈ 2 - 1.699 = 0.301, illustrating how lower %T yields higher absorbance. The other forms don’t match this relationship because they omit the division by 100 inside the log or otherwise alter the constant.