If they overlap and same spatial reference, use Mosaic To New Raster—Help | ArcGIS for Desktop tool and make the mosaic operator refer to Ras2 in your input raster sort, as the following picture.
The MosaicDataset Fan is back: You should create a MosaicDataset and load both. Where one has a higher resolution than the other - it will be used - thats the simple version. There is a lot you can set as properties, too. No need to calculate them into a new dataset, if you dont want to. Though thats an option, no doubt.
Thanks for the answer Gunter. My only issue is that I have no access to the right licence to create a Mosaic Dataset under Data Management. Therefore I will follow Abdullah and Dan's advice.
Really appreciate though
Thanks for the reply. Yes - it requires at least Standard licensing. If you work a lot with rasters it might be worth it just because of that. Hope you have success with the procedures described by Dan and Abdullah