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.

This section provides additional calculators useful for exploring photochemistry and light-matter interactions:

• Monochromatic Calculator: Analyze the simplest case with a single wavelength. Includes calculators for Napierian absorptivity, absorbance, and effective half-life at a given concentration and pathlength.
• Multiwavelength Calculator: Extend analysis to polychromatic light sources. Compute wavelength-dependent absorption, incident and absorbed photons, and explore effects of spectral shape on photochemical processes.
• Broadband Calculator: Model real-world sources with broad spectral distributions. Allows integration over the full spectrum to quantify total absorbed photons and compare different light sources.

These calculators build on each other sequentially: start with the simple monochromatic case, then progress to multiwavelength, and finally broadband analysis for more realistic scenarios.