In fluorescence, the luminescent intensity IF is proportional to the excited state population (the number of molecules in excited states). The excited state population, in turn, is proportional to the radiation absorbed by the sample. However, all the molecules present at the excited state do not participate in the fluorescence process. Therefore, IF is proportional to the fluorescence efficiency or fluorescence quantum yield, ΦF, also. If one replaces the number of photons absorbed at the excitation wavelength by the absorbed intensity, I_A, then

I_f α φ_fI_a,orI_f = kφ_fI_a

where the proportionality factor k depends on several instrumental parameters.

If I₀ is the incident beam intensity and I_T is the transmitted beam intensity, then

I_a=I₀−I_T

In fluorescence, the luminescent intensity I_F is proportional to the excited state population (the number of molecules in excited states). The excited state population, in turn, is proportional to the radiation absorbed by the sample. However, all the molecules present at the excited state do not participate in the fluorescence process. Therefore, I_F is proportional to the fluorescence efficiency or fluorescence quantum yield, φ_F, also. If one replaces the number of photons absorbed at the excitation wavelength by the absorbed intensity, I_A, then According to the Beer-Lambert law as applicable to the absorption of radiation by the sample:

I_T/I₀=10^−εcl=e^−εcl

where I_T is the intensity of the transmitted light, ε is the molar absorptivity of the analyte, c is the molar concentration of the analyte, and l is the optical pathlength of the sample. Therefore,

I_A=I₀−I_T=I₀−I₀.10_{−εcl=I0(1−e−2.3εcl)}

and

I_F=kφ_FI₀(1−e_−2.3εcl)

If εcl (i.e. absorbance, A) is small (say, 0.05 or less) in the above equation, expanding the exponential series and neglecting the higher order terms in the series one gets,

IF≈2.3kφFI0εcl.

Therefore, when the absorbance is small, fluorescence intensity is proportional to the concentration of the fluorophore. That is, there is a linear relationship between fluorescence intensity and the concentration of the fluorophore. One can construct a linear calibration plot of fluorescence intensity (I_F ) vs. fluorescent analyte concentration (c) which can be used for the determination of an unknown concentration of a fluorescent analyte. This provides a sensitive method for quantitative fluorimetry.

Note that though φF is independent of wavelength since φ is wavelength-dependent, fluorescence intensity, IF, is also wavelength-dependent. If I_F is measured as a function of the wavelength of exciting light of constant intensity I0, the resulting variation in fluorescence intensity with respect to the excitation light wavelength is called fluorescence excitation spectrum. This fluorescence excitation spectrum, reflect s the variation in ε, molar extinction coefficient, as a function of wavelength and therefore essentially reproduce the absorption spectrum of the molecule.

Further, the absorbance to be small, the absorptivity and the concentration of the fluorophore must be small (very dilute solution). At higher concentrations, concentration quenching may give rise to nonlinear relationship. Another important point should be noted here. The fluorescence intensity is usually plotted in arbitrary units. In the above equation, the proportionality constant, k, is an instrumental factor. It depends on many parameters like the geometry of observation (i.e., solid angle through which the light is collected), monochromator transmission efficiency, monochromator slit-width, high voltage of the photo-multiplier, gain of the electronic devices, etc. Therefore, the numerical value of the measured fluorescence intensity has no meaning and the fluorescence spectrum is usually plotted in arbitrary units unlike the absorption spectrum . It is also important to remember that in addition to the above mathematical reason, the fluorescence intensity-concentration linear relationship is valid over only a limited range of absorbances due to inner filter effects caused by geometrical reasons (i.e., geometry of the sample cell arrangement ) or presence of other chromophores.

In this experiment, we shall determine the concentration of quinine in tonic water spectrofluorimetrically with the help of a calibration plot made by using quinine sulfate standard solutions. Quinine is a strongly fluorescent compound in dilute acid solution. It is commonly used as a fluorescence standard. Quinine is also used as an antimalarial drug and a common ingredient in tonic water and soft drinks. Often tonic water contains 40 - 85 ppm quinine. Quinine is a natural product (alkaloid) isolated from the bark of the cinchona tree.