Context : Scattering processes in the atmospheres of planets cause characteristic features that can be particularly well observed in polarisation .
For planet Earth , both molecular scattering ( Rayleigh ) and scattering by small particles ( Mie ) imprint specific signatures in its phase curve .
Polarised phase curves allow us to infer physical and chemical properties of the atmosphere like the composition of the gaseous and liquid components , droplet sizes , and refraction indices .

Aims : An unequivocal prediction of a liquid-water-loaded atmosphere is the existence of a rainbow feature at a scattering angle of around 138-144 ^ { \circ } .
Earthshine allows us to observe the primary rainbow in linear polarisation .

Methods : We observed polarisation spectra of Earthshine using FORS2 at the Very Large Telescope for phase angles from 33 ^ { \circ } to 65 ^ { \circ } ( Sun–Earth–Moon angle ) .
The spectra were used to derive the degree of polarisation in the B , V , R , and I passbands and the phase curve from 33 ^ { \circ } to 136 ^ { \circ } .
The new observations extend to the smallest phases that can be observed from the ground .

Results : The degree of polarisation of planet Earth is increasing for decreasing phase angles downwards of 45 ^ { \circ } in the B , V , R , and I passbands .
From comparison of the phase curve observed with models of an Earth-type atmosphere we are able to determine the refractive index of water and to constrain the mean water droplet sizes to 6 - 7 \mu m. Furthermore , we can retrieve the mean cloud fraction of liquid water clouds to 0.3 , and the mean optical depth of the water clouds to values between 10 and 20 .

Conclusions : Our observations allow us to discern two fundamentally different scattering mechanisms of the atmosphere of planet Earth : molecular and particle scattering .
The physical and chemical properties can be retrieved with high fidelity through suitable inversion of the phase curve .
Observations of polarimetric phase curves of planets beyond the Solar System shall be extremely valuable for a thorough characterisation of their atmospheres .