Aims. We present the first multi-epoch N-band spectro-interferometric observations of the carbon-rich Mira variable V Oph using MIDI at the ESO's Very Large Telescope Interferometer. Our aim is to study temporal variations of physical properties of the outer atmosphere and the circumstellar dust shell based on spectrally-dispersed N-band visibilities over the C2H2 (+HCN) features and the dust emission. Methods. Our MIDI observations were carried out at three different phases 0.18, 0.49, and 0.65, with three different baselines ( projected baseline lengths of 42-124 m) using four 8.2 m Unit Telescopes ( UT2-UT4, UT1-UT4, and UT2-UT3 baseline configurations). Results. The wavelength dependence of the uniform-disk diameters obtained at all epochs is characterized by a roughly constant region between 8 and 10 mu m with a slight dip centered at similar to 9.5 mu m and a gradual increase longward of 10 mu m. These N-band angular sizes are significantly larger than the estimated photospheric size of V Oph. The angular sizes observed at different epochs reveal that the object appears smaller at phase 0.49 ( minimum light) with uniform-disk diameters of similar to 5-12 mas than at phases 0.18 (similar to 12-20 mas) and 0.65 (similar to 9-15 mas). We interpret these results with a model consisting of optically thick C2H2 layers and an optically thin dust shell. Our modeling suggests that the C2H2 layers around V Oph are more extended (similar to 1.7-1.8 R-*) at phases 0.18 and 0.65 than at phase 0.49 (similar to 1.4 R-*) and that the C2H2 column densities appear to be the smallest at phase 0.49. We also find that the dust shell consists of amorphous carbon and SiC with an inner radius of similar to 2.5 R-*, and the total optical depths of tau(v) approximate to 0.6-0.9 ( tau(11.3) mu m approximate to 0.003 and 0.004 for amorphous carbon and SiC, respectively) found at phases 0.18 and 0.65 are higher than the value obtained at phase 0.49, tau(v) approximate to 0.3 ( tau(11.3) mu m approximate to 0.001 and 0.002 for amorphous carbon and SiC, respectively). Conclusions. Our MIDI observations and modeling indicate that carbon- rich Miras also have extended layers of polyatomic molecules as previously confirmed in oxygen-rich Miras. The temporal variation of the N-band angular size is largely governed by the variations of the opacity and the geometrical extension of the C2H2 layers and the dust shell, and consequently, this masks the size variation of the photosphere. Also, the observed weakness of the mid-infrared C2H2 absorption in carbon- rich Miras can be explained by the emission from the extended C2H2 layers and the dust shell.
