Non-parallel absorption and emission transition moments

This situation occurs when excitation brings the fluorophores to an excited state other than the first singlet state from which fluorescence is emitted. Let a be the angle between the absorption and emission transition moments. The aim is to calculate cos dE and then to deduce r by means of Eq. (5.20). 

According to the classical formula of spherical trigonometry, cos dE can be written as 

By taking the square of the two sides of Eq. (5.25) and taking into account the fact that all values of y/ are equiprobable (cos y/ = 0 cos2 y/ = 1/2), we obtain 

The case of indole and tryptophan is peculiar because the low-lying absorption bands overlap. Box 5.2 shows how the indole absorption spectrum can be resolved into two bands from the combined measurement of the excitation spectrum and the exdtation polarization spectrum. 

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