## magic angle

https://doi.org/10.1351/goldbook.MT07419
Upon excitation of an 'isotropic' sample (assuming an ultra short excitation pulse) the relationship between the fluorescence intensity detected at a time t and through a polarization analyser oriented at an angle β with respect to the electric polarization of the exciting beam is given by $I(t,\beta ) \propto N(t)\left [ 1 + (3\, \text{cos}^{2}\, \beta - 1)R(t) \right ]$ where R(t) is the degree of alignment of the emitting transition dipole in the laboratory frame and N(t) is the excited-state population, both at time t. For β = 54.7° (the magic angle), the dipole-alignment contribution vanishes and I(t,β=54.7°) ∝ Nt.
Notes:
1. This concept also applies for time-resolved absorption measurements in cases in which @PT07461@ occurs because the detected species do not freely rotate fast enough to make the measurement @I03353@ within the time of the experiment.
2. Applies for steady-state measurements on fixed samples. In this case $I(\beta ) \propto N\left [ 1 + (3\, \text{cos}^{2}\, \beta - 1)R \right ]$ with $$I(\beta)$$ the intensity of the effect observed at an analyser @A00346@ $$\beta$$ with respect to the electric @P04712@ of the exciting beam, $$N$$ the excited-state population at steady-state equilibrium, and $$R$$ the degree of alignment of the @T06460@ of the excited molecular entity.
3. The term magic @A00346@ is also used in NMR @S05848@.
Source:
PAC, 2007, 79, 293. 'Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)' on page 367 (https://doi.org/10.1351/pac200779030293)