Absorption phenomenon

Interaction of electromagnetic radiation, including light, with matter is fairly universal across its broad spectrum.  Because of the role vision and color play in human life, it is easier to illustrate and visualize such phenomenon in the region of spectrum that human eye is sensitive to, called visible spectrum.

Why light is absorbed

A quantum of light has dual nature: it is a discrete particle and electromagnetic wave. Electromagnetic nature of a photon allows it to interact with charged particles such as atomic nucleae and electrons.  According to quantum physics, molecules and atoms can exist in discrete states which are different in energy. Photon can be absorbed by a molecule when energy of photon travelling thorough an electron cloud happens to match the difference in energy between two states of that molecule.

Energy of photons in the visible region of spectrum usually corresponds to the difference in energy levels of an outer electron(s) in a molecule and therefore is called electronic absorption. In the infrared region low-energy photons would match difference in energy between two different mode of vibration of atoms in a molecule and this is called vibrational absorption.

Each molecule in each of its possible states is characterized by a unique set of possible energy differences, or transitions. These transitions can be considered as fingerprints of a specific molecule or a related group. An example is how green color is associated with plants because of light absorption by chlorophyll and red color is associated with blood and flesh due to light absorption by heme in hemoglobin and myoglobin.  While typical human eye can distinguish small changes in light absorption as color variations, it is not the most sensitive or accurate tool for quantitative analysis. Modern spectroscopic instruments allow to register much smaller changes across broader range and to use these minute changes in analysis.   

 Light measurements

As light travels through matter is gets absorbed. Such disappearance is commonly expressed in units of either transmission or absorption. Both forms expresses change in a measure (light intensity), or a ratio, and thus is dimensionless. In most cases absorption does not depend on the amount of incident light, unless light itself causes changes in the sample, which is called photoreactivity.

Transmission of a substance is a ratio of intensity of light passed through this substance I to intensity of incident light I₀.
T = I/I₀
Transmission is often expressed in %.  Nowadays transmission is not used often in optical measurements because it cannot adequately represent sensitivity of modern instruments.

Absorption (the measure) is another form of representing absorption of light (the phenomenon) by substances. Absorption if defined as a negative logarithm of transmission.

A = -log₁₀(I/I₀)

Absorption is a much more practical measure than transmission. First, it is proportional to basic sample parameters, as described below. Second, it allows to analyze absorption properties over great dynamic range by magnifying small changes and leveling off big changes. Keep in mind that larger absorption value means that less light is transmitted and zero absorption means all light is transmitted. 

Beer-Lambert law

Fraction of light that is absorbed by sample is described by a Beer-Lambert law, which is instrumental to any spectroscopic measurement due to its simplicity. According to this law, absorption by a substance is proportional to substance concentration C and the distance light travels l with linear coefficient e:
A = e × c × l

From Bee-Lambert law it follows that absorption will double with each doubling of sample concentration. 

The travel distance is called a pathlength. Standard pathlength is historically 1 cm.  Most cuvettes for optical measurements are manufactured with high accuracy to this standard.

The proportionality coefficient e is called coefficient of molar extinction. It is one of fundamental properties of substances and therefore can be used as a measure of substance concentration for known pathlength. Molar extinction coefficient is wavelength dependent. Its value at each wavelength depends on the probability of a transition between two quantum mechanical states with the energy difference equal to the energy of photon at that wavelength. Because molecules of each substance have a unique combination all possible transitions, extinction coefficients at various wavelengths combine into a unique spectrum that is a fingerprint of such substance.  Changes in extinction coefficients across visible region of spectrum are responsible for preferential absorption of one wavelength over another that gives world color in our perception.  

Importance of Beer-Lambert law is fundamental for spectroscopy. It allows to predict absorption of a known sample, determine sample concentration, identify and measure components in complex mixtures etc.