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With assumptions that the violation of the distance-duality (DD) relationentirely arises from non-conservation of the photon number and the absorptionis frequency independent in the observed frequency range, we performcosmological-model-independent tests for the cosmic opacity. The observationaldata include the largest Union2.1 SN Ia sample, which is taken for observed$D_\mathrm{L}$, and galaxy cluster samples compiled by De Filippis {\it et al.}and Bonamente {\it et al.}, which are responsible for providing observed$D_\mathrm{A}$. Two parameterizations, $\tau(z)=2\epsilon z$ and$\tau(z)=(1+z)^{2\epsilon}-1$ are adopted for the optical depth associated tothe cosmic absorption. We find that, an almost transparent universe is favoredby Filippis {\it et al.} sample but it is only marginally accommodated byBonomente {\it et al.} samples at 95.4% confidence level (C. L.) (even at 99.7%C. L. when the $r<100 \mathrm{kpc}$-cut spherical $\beta$ model is considered).Taking the possible cosmic absorption (in 68.3% C. L. range) constrained fromthe model-independent tests into consideration, we correct the distance modulusof SNe Ia and then use them to study their cosmological implications. Theconstraints on the $\Lambda$CDM show that a decelerating expanding universewith $\Omega_\Lambda=0$ is only allowed at 99.7% C. L. by observations when theBonamente {\it et al.} sample is considered. Therefore, our analysis suggeststhat an accelerated cosmic expansion is still needed to account for the dimmingof SNe and the standard cosmological scenario remains to be supported bycurrent observations.

Cosmic opacity: cosmological-model-independent tests and their impacts on cosmic acceleration