For a photo-induced process to proceed, light must be absorbed. Consequently, the light intensity in photosensitive media decreases with depth. This interactive graph demonstrates the relationship between key variables.

Attenuation model
$$ \frac{dI}{dz} = -I \, \varepsilon \, [C] $$ $$ \frac{I}{I_0} = \exp\!\big(-\varepsilon \, [C] \, z\big) $$ \( I \) – intensity at depth \( z \) \((\text{mW/cm}^2)\)
\( I_0 \) – incident intensity \((\text{mW/cm}^2)\)
\( \varepsilon \) – Napierian molar extinction coefficient \((\text{L/mol·cm})\)
\( [C] \) – chromophore concentration \((\text{mol/L})\)
\( z \) – depth \((\mu\text{m})\)
Adjusting for wavelength
The energy of a photon is inversely proportional to the wavelength \(\lambda\). This relationship is useful for converting light intensity from \((\text{mW/cm}^2)\) to \((\text{Einstein/s·cm}^2)\), where \(1 \ \text{Einstein} = 1 \ \text{mol photons}\) when events must be counted, such as for initiator half-life. $$ E = \frac{h \, c \, N_A}{\lambda} $$ \( E \) – photon energy \((\text{J/mol})\)
\( h \) – Planck's constant \((6.6261 \times 10^{-34} \ \text{J·s})\)
\( c \) – speed of light \((2.9979 \times 10^{8} \ \text{m/s})\)
\( N_A \) – Avogadro's number \((6.022 \times 10^{23} \ \text{mol}^{-1})\)
\( \lambda \) – wavelength of light \((\text{nm})\)

This simulation was created in the Department of Chemical and Biological Engineering at University of Colorado Boulder for LearnChemE.com by Alexander Osterbaan under the direction of Professor John L. Falconer and Professor Christopher N. Bowman and with the assistance of Drew Smith and Meagan Arguien. Address any questions or comments to LearnChemE@gmail.com.