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Why does light intensity decrease exponentially as light travels through an absorbing material?

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Diagram of a tree leaf illustrating photosynthesis, with arrows showing sunlight, water, and carbon dioxide entering the leaf and sugars and oxygen being produced. A person is shown beside the tree to demonstrate the exchange of oxygen and carbon dioxide between plants and animals. — electromagnetic radiation Diagram of photosynthesis showing how water, light, and carbon dioxide are absorbed by a plant to produce oxygen, sugars, and more carbon dioxide.

Light intensity decreases exponentially as it travels through an absorbing material because each successive, equally thin layer of the medium absorbs a constant fraction of the energy that reaches it.12

This process can be visualized by considering a homogeneous substance as a series of thin layers. If a specific layer absorbs a fixed percentage of the incident energy, the remaining energy entering the next layer is reduced by that same proportion. Consequently, the energy does not decrease linearly; rather, the amount of energy lost in each subsequent layer is smaller than the amount lost in the previous one, as there is less energy available to be absorbed.1

This relationship is fundamental to the study of absorption and is often described by the Beer-Lambert law, which relates the reduction of radiant energy to the path length and the properties of the medium. The rate of this energy loss is determined by the material's absorption coefficient, which remains constant for a given wavelength.341