Context :

Aims : We present the first detection of diffuse dust in the intra-cluster medium of the Virgo cluster out to \sim 0.4 virial radii , and study the radial variation of its properties on a radial scale of the virial radius .

Methods : Analysing near-UV - i colours for a sample of \sim 12000 background galaxies with redshifts 0.02 < z < 0.8 , we find significant colour reddening and relate it to variation in E ( B - V ) values .

Results : The E ( B - V ) mean profile shows a dust component characterised by an average reddening E ( B - V ) \sim 0.042 \pm 0.004 mag within 1.5 degrees ( \sim 0.3 r _ { vir } ) from the cluster centre .
Assuming a Large Magellanic Cloud extinction law , we derive an average visual extinction A _ { V } = 0.14 \pm 0.01 for a total dust mass , M _ { d } = 2.5 \pm 0.2 \times 10 ^ { 9 } M _ { \odot } , hence a dust-to-gas mass ratio M _ { d } / M _ { g } = 3.0 \pm 0.3 \times 10 ^ { -4 } .
Based on the upper limits on the flux density \mathrm { I _ { 250 \mu m } = 0.1 MJysr ^ { -1 } } derived from Herschel data , we estimate an upper limit for the dust temperature of T _ { d } \sim 10 K .
However , similar densities can be obtained with dust at higher temperatures with lower emissivities .

Conclusions : The Virgo cluster has diffuse dust in its intra-cluster medium characterised by different physical properties as those characterising the Milky Way dust .
The diffuse dust in Virgo is transported into the cluster space through similar phenomena ( stripping ) as those building up the optical intra-cluster light , and it constitutes an additional cooling agent of the cluster gas .