A dye absorbs a photon of wavelength $\mathrm{\lambda }$ and re-emits the same energy into two photons of wavelengths ${\mathrm{\lambda }}_{1}$ and ${\mathrm{\lambda }}_{2}$ respectively. The wavelength $\mathrm{\lambda }$ is related with ${\mathrm{\lambda }}_{1}$ and ${\mathrm{\lambda }}_{2}$ as:

1.  $\mathrm{\lambda }=\frac{{\mathrm{\lambda }}_{1}+{\mathrm{\lambda }}_{2}}{{\mathrm{\lambda }}_{1}{\mathrm{\lambda }}_{2}}$

2.  $\mathrm{\lambda }=\frac{{\mathrm{\lambda }}_{1}{\mathrm{\lambda }}_{2}}{{\mathrm{\lambda }}_{1}+{\mathrm{\lambda }}_{2}}$

3.  $\mathrm{\lambda }=\frac{{\mathrm{\lambda }}_{1}^{2}+{\mathrm{\lambda }}_{2}^{2}}{{\mathrm{\lambda }}_{1}+{\mathrm{\lambda }}_{2}}$

4.  $\mathrm{\lambda }=\frac{{\mathrm{\lambda }}_{1}{\mathrm{\lambda }}_{2}}{{\left({\mathrm{\lambda }}_{1}+{\mathrm{\lambda }}_{2}\right)}^{2}}$

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