If you have purified recombinant protein from bacterial lysates and just want to check qualitatitvely, then the quick and dirty method is to run it on the agarose gel and stain with gel red or pico green or EtBr. Also you could resuspend well and run protein on PAGE, if they gel has smiles with joker-like ends (thickened ends of the band), it has some DNA contamination. The other method is of course to use DNA intercalating florescent dyes and quantification.
Thank you very much for your reply, the discussion is very interesting.
I found this paper (enclosed) explaining that; originally, the ratio 260/280 is more to evaluate the contamination of protein prep by DNA. But we usually do the reverse, in order to assess the protein contamination of DNA prep. However, the enclosed document explains well that this is not very accurate because epsilon of DNA is bigger than epsilon of protein at 260 or 280 nm. Therefore, the ration 260/280 is more accurate to assess the DNA contamination in protein prep than to assess protein contamination in DNA prep...