Just a follow-up about some of the names... I accidentally separated "chromic acid" from "Jones' reagent" like they were two different things, but Jones' reagent is often called "chromic acid reagent" also. The name "chromic acid" refers to the compound H2CrO4, (not yet actually isolated, I gather), which in principle can form from the reaction of CrO3 with water. For this reason, CrO3 is often called "chromic anydride", or, unfortunately, "chromic acid" again, which is really misleading! Jones' reagent is prepared by mixing CrO3, concentrated H2SO4, and water. It can be used in acetone solvent to oxidize water-insoluble compounds, and double bonds are normally not attacked. (This may be why KMnO4 is less popular, as it oxidizes double bonds also, making it a less selective oxidant.)
A similar chromium reagent is often prepared by using sodium dichromate, Na2Cr2O7, instead of CrO3, to make the reagent, but this is not called Jones' reagent. It too is often confusingly called "chromic acid". In principle, the dichromate ion can be protonated by H2SO4 to form "dichromic acid", H2Cr2O7 (another unisolated compound) which can react with water to form 2H2CrO4, chromic acid.
So I guess in general we can call any reagent made from Na2CrO4, Na2Cr2O7, or CrO3 "chromic acid" reagent, although the exact species in each solution may be different compounds with uncertain formulas, probably existing in complex equilibria. In my own experience I've found that Jones' reagent works most reliably for testing 1°, 2°, and 3° alcohols. For some reason I always got less consistent results with dichromate reagents, even though they are used a lot in oxidations of organic compounds.
Steve